Question

You have $51,983.14 in a brokerage account, and you plan to deposit an additional $3,000 at the end of every future year until your account totals $250,000. You expect to earn 11% annually on the account. How many years will it take to reach your goal? Round your answer to the nearest whole number. years What's the future value of an 8%, 5-year ordinary annuity that pays $100 each year? If this was an annuity due, what would its future value be? Do not round intermediate calculations. Round your answers to the nearest cent. Future Value of an ordinary Annuity: $ Future Value of an Annuity Due: $ An investment will pay $50 at the end of each of the next 3 years, $200 at the end of Year 4, $400 at the end of Year 5, and $600 at the end of Year 6. If other investments of equal risk earn 10% annually, what is its present value? Its future value? Do not round intermediate calculations. Round your answers to the nearest cent. Present value: $ Future value: $ You want to buy a car, and a local bank will lend you $15,000. The loan will be fully amortized over 5 years (60 months), and the nominal interest rate will be 12% with interest paid monthly. What will be the monthly loan payment? What will be the loan's EAR? Do not round intermediate calculations. Round your answer for the monthly loan payment to the nearest cent and for EAR to two decimal places. Monthly loan payment: $ EAR: %

Answer 1

Answer to Question 1:

Current Balance of Account = $51,983.14
Annual Deposit = $3,000
Desired Balance of Account = $250,000
Annual Interest Rate = 11%

Let it will take n years to achieve the desired balance of account.

$51,983.14 * FV of $1 (11%, n) + $3,000 * FVA of $1 (11%, n) = $250,000

Using financial calculator:
I = 11%
PV = -51983.14
PMT = -3000
FV = 250000

N = 12

So, it will take 12 years to achieve the desired balance of account.

Answer to Question 2:

Annual Deposit = $100
Annual Interest Rate = 8%
Period = 5 years

Future Value of an Ordinary Annuity = $100*1.08^4 + $100*1.08^3 + $100*1.08^2 + $100*1.08 + $100
Future Value of an Ordinary Annuity = $100 * (1.08^5 - 1) / 0.08
Future Value of an Ordinary Annuity = $100 * 5.8666
Future Value of an Ordinary Annuity = $586.66

Future Value of an Annuity Due = $100*1.08^5 + $100*1.08^4 + $100*1.08^3 + $100*1.08^2 + $100*1.08
Future Value of an Annuity Due = $100 * 1.08 * (1.08^5 - 1) / 0.08
Future Value of an Annuity Due = $100 * 6.3359
Future Value of an Annuity Due = $633.59