You would like to save annually for buying a car 6 years from today. Suppose the...
You would like to save annually for buying a car 6 years from today. Suppose the first deposit is made today and the last deposit will be made 5 years from now. Assume the car will cost you $30,000 and your deposits earn you interest at 6% p.a. compounded annually.
a. What is your annual deposit amount?
b. Instead of making annual deposits, you would like to make your deposit monthly and the bank is happy to pay your interest on a monthly basis. What is the APR that would make the bank indifferent to these two way of paying interest?
c. Assuming you make the deposit of $300 at the end of each month and the first deposit will be made one month from today, use the answer to part b calculate how much your deposits would accumulate to 6 years later
d. Assume 6 years later, the car price has gone up to $35,000. You decide to use the accumulated deposit as the down payment and take up a 2-year car loan. What would your monthly payment be if the interest rate is 7.5% and compounded monthly?
(Show the working and formulas for each answers)
Homework Answers
| Rate | Annual interest rate | 6% | ||||||||
| Nper | Number of annual deposit | 6 | ||||||||
| Fv | Future Value required | $30,000 | ||||||||
| Type | Deposit at the beginning of year | 1 | ||||||||
| PMT | Annual Deposit Required | $4,057.43 | (Using PMT function of excel with Rate=6%,Nper=6,Fv=-30000,Type=1) | |||||||
| b | Monthly Deposit | |||||||||
| Nper | Number of monthly deposit =6*12 | 72 | ||||||||
| Pmt | Monthly deposit =4057/12= | $338.12 | ||||||||
| Fv | Future Value required | $30,000 | ||||||||
| RATE | Monthly interest rate required | 0.57% | (Using RATE function of excel withNper=72,Pmt=-338.12Fv=30000) | |||||||
| APR that will make the bank indifferent | 6.84% | (0.57%*12) | ||||||||
| c | If $300 is deposited per month | |||||||||
| Nper | Number of monthly deposit =6*12 | 72 | ||||||||
| Rate | Monthly interest rate | 0.57% | ||||||||
| Pmt | Monthly deposit | $300 | ||||||||
| FV | Accumulated amount at end of 6 years | $26,617.82 | (Using FV function of excel with Rate=0.57%,Nper=72,Pmt=-300) | |||||||
| d | ||||||||||
| Down Payment | $26,617.82 | |||||||||
| Pv | Loan amount =35000-26617.82= | $8,382.18 | ||||||||
| Rate | Monthly interest rate=(7.5/12)% | 0.625% | ||||||||
| Nper | Number of months of loan repayment | 24 | ||||||||
| PMT | Monthly Payment Required | $377.19 | (Using PMT function of excel with Rate=0.625%,Nper=24,Pv=-8382.18) | |||||||
    |
||||||||||
Add Answer to:
You would like to save annually for buying a car 6 years from
today. Suppose the...
1. You would like to save $70 000 in 10 years. To accumulate this amount, you...
1. You would like to save $70 000 in 10 years. To accumulate this amount, you plan to make a regular deposit with an equal amount of cash into a saving account at the end of each year. This account will earn 6% p.a interest compounded annually. Your first payment will be made at the end of this year. a. How much must you deposit annually to accumulate this amount in 10 years? b. If you decide to make a...
Complex present value) You would like to have $56 comma 000 in 16 years. To accumulate...
Complex present value) You would like to have $56 comma 000 in 16 years. To accumulate this amount you plan to deposit each year an equal sum in the bank, which will earn 6 percent interest compounded annually. Your first payment will be made at the end of the year. a. How much must you deposit annually to accumulate this amount? b. If you decide to make a large lump-sum deposit today instead of the annual deposits, how large should...
Suppose you are exactly 25 years old and you are planning to save for your retirement...
Suppose you are exactly 25 years old and you are planning to save for your retirement which will happen in 40 years. You plan to deposit equal amount at the beginning of each month in your retirement account with the first saving made today. Assume the retirement account pays you 6% p.a. compounded monthly. (a) If you would like to have $1,000,000 in your retirement account 40 years later when you are retired, how much will you have to deposit...
In 4 years you would like to have $5141 for a down payment for a car....
In 4 years you would like to have $5141 for a down payment for a car. The local bank is paying 2% interest, compounded annually. How much would you need to deposit today to reach your goal of $5141? Enter your answer as follows: 1234 Round your answer. Do not use a dollar sign("$", a comma(" or any decimal points(")
(Complex present value) You would like to have $30,000 in 16 years. To accumulate this amount...
(Complex present value) You would like to have $30,000 in 16 years. To accumulate this amount you plan to deposit each year an equal sum in the bank, which will earn 7 percent interest compounded annually. Your first payment will be made at the end of the year. a. How much must you deposit annually to accumulate this amount? b. If you decide to make a large lump-sum deposit today instead of the annual deposits, how large should this lump-sum...
1) (3 pts) Bob would like to have a total savings of $30,000 in 6 years...
1) (3 pts) Bob would like to have a total savings of $30,000 in 6 years to use as a down payment on a future house purchase. He has no money saved up now, but plans on depositing $350 per month at the end of every month to save for this goal. What is the periodic interest rate Bob must earn to reach his goal? What is the Annual Percentage rate? 1 Periodic *.ㅡ I Nominal (APR)- % 2) (3...
please answer all of the following questions 25. You currently owe $26,000 on a car loan...
please answer all of the following questions
25. You currently owe $26,000 on a car loan at 4.25 percent interest. If you make monthly payments of $596.59 per month, how long i.e., number of months rounded to one decimal place) will it take you to fully repay the loan? 26. It is now January 1. You plan to make 5 deposits of $300 each, one every 6 months, with the first payment being made exactly six months from today. If...
You must make a payment of $3,800 exactly 8 years from today. To prepare for this...
You must make a payment of $3,800 exactly 8 years from today. To prepare for this payment, you will make 5 equal deposits into an account that pays a nominal interest rate of 7.6% p.a., with quarterly compounding. If your first deposit is made today (and then you make four additional deposits in each of the next four quarters – that is, a deposit 3 months from today, another 6 months from today and so on), what must each of...
1. Suppose you accumulated $500,000, perhaps from many years of saving. You put the money in...
1. Suppose you accumulated $500,000, perhaps from many years of saving. You put the money in a savings plan earning 6% compounded monthly. If you want to withdraw $4,000 at the beginning of each month, how long before the savings plan is exhausted? 2. Suppose you accumulated $500,000, perhaps from many years of saving. You put the money in a savings plan earning 6% compounded monthly. If you want the plan to last 40 years, how much can you withdraw...
please answer all of the following questions 21. Suppose you deposit $5,000 into an account earning...
please answer all of the following questions
21. Suppose you deposit $5,000 into an account earning 4 percent interest, compounded monthly and you also make monthly contributions of $50 (first monthly contribution made one month after the initial deposit is made). How many years (rounded to one decimal place --for example, 32.1843 year = 32.2) will it take for the account to grow to $7,500 in this case? 22. Assume that I am trying to borrow money from you to...
1. You would like to save $70 000 in 10 years. To accumulate this amount, you plan to make a regular deposit with an equal amount of cash into a saving account at the end of each year. This account will earn 6% p.a interest compounded annually. Your first payment will be made at the end of this year. a. How much must you deposit annually to accumulate this amount in 10 years? b. If you decide to make a...
In 4 years you would like to have $5141 for a down payment for a car. The local bank is paying 2% interest, compounded annually. How much would you need to deposit today to reach your goal of $5141? Enter your answer as follows: 1234 Round your answer. Do not use a dollar sign("$", a comma(" or any decimal points(")
(Complex present value) You would like to have $30,000 in 16 years. To accumulate this amount you plan to deposit each year an equal sum in the bank, which will earn 7 percent interest compounded annually. Your first payment will be made at the end of the year. a. How much must you deposit annually to accumulate this amount? b. If you decide to make a large lump-sum deposit today instead of the annual deposits, how large should this lump-sum...
1) (3 pts) Bob would like to have a total savings of $30,000 in 6 years to use as a down payment on a future house purchase. He has no money saved up now, but plans on depositing $350 per month at the end of every month to save for this goal. What is the periodic interest rate Bob must earn to reach his goal? What is the Annual Percentage rate? 1 Periodic *.ㅡ I Nominal (APR)- % 2) (3...
please answer all of the following questions
25. You currently owe $26,000 on a car loan at 4.25 percent interest. If you make monthly payments of $596.59 per month, how long i.e., number of months rounded to one decimal place) will it take you to fully repay the loan? 26. It is now January 1. You plan to make 5 deposits of $300 each, one every 6 months, with the first payment being made exactly six months from today. If...
please answer all of the following questions
21. Suppose you deposit $5,000 into an account earning 4 percent interest, compounded monthly and you also make monthly contributions of $50 (first monthly contribution made one month after the initial deposit is made). How many years (rounded to one decimal place --for example, 32.1843 year = 32.2) will it take for the account to grow to $7,500 in this case? 22. Assume that I am trying to borrow money from you to...
Most questions answered within 3 hours.
-
A coach uses a new technique to train gymnasts. Seven
gymnasts were randomly selected and their...
asked 58 minutes ago -
While rotating the tires on your car you notice a rock [mass =
0.1 Kg] stuck...
asked 2 hours ago -
Using MARS simulator, write MIPS programs according to
the following scenarios: Receive a positive integer number...
asked 4 hours ago -
An object in front of a concave mirror has a real image that is
11.5 cm...
asked 5 hours ago -
Consider the reaction, C3 H8 + O2 --> CO2 + H2O. How many
moles of O2...
asked 6 hours ago -
You and your opponent both roll a fair die. If you both roll the
same number,...
asked 7 hours ago -
In a study of the accuracy of fast food drive-through orders,
Restaurant A had 257 accurate...
asked 7 hours ago -
Identify and describe in detail the four categories of
institutions that could be included in a...
asked 7 hours ago -
In python
class Customer:
def __init__(self, customer_id, last_name, first_name, phone_number, address):
self._customer_id = int(customer_id)
self._last_name =...
asked 7 hours ago -
What is an example of a limitation in implementing a new
ERP system and how it...
asked 7 hours ago -
In a section of 9.7cm of an artery with a radius of 2.6mm there
is a...
asked 7 hours ago -
the two carboxylic acid groups of aspartic acid have different
acidities with pKa values of 2.1...
asked 7 hours ago