Question

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1. Susan Wilson is a sales executive at a Baltimore firm. She is 25 years old and plans to invest $3,800 every year in an IRA account, beginning at the end of this year until she reaches the age of 65. If the IRA investment will earn 8.45percent annually, how much will she have in 40 years, when she turns 65? (Round answer to 2 decimal places)

2. Donna Clark is a sales executive at a Baltimore firm. She is 25 years old and plans to invest $2,500 each year in an IRA account until she is 65 at which time she will retire (a total of 40 payments). If Donna invests at the beginning of each year, and the IRA investment will earn 11.00 percent annually, how much will she have when she retires? Assume that she makes the first payment today.(Round answer to 2 decimal places)

3. Kevin Hall is saving for an Australian vacation in three years. He estimates that he will need $5,920 to cover his airfare and all other expenses for a week-long holiday in Australia. If he can invest his money in an S&P 500 equity index fund that is expected to earn an average annual return of 10.5 percent over the next three years, how much will he have to save every year if he starts saving at the end of this year?

4.Your grandfather is retiring at the end of next year. He would like to ensure that his heirs receive payments of $9,600 a year forever, starting when he retires. If he can earn 6.1 percent annually, how much does your grandfather need to invest to produce the desired cash flow? (Round answer to 2 decimal places)

5.Joseph Moore borrowed $15,550 from a bank for three years. If the quoted rate (APR) is 8.90 percent, and the compounding is daily, what is the effective annual interest rate (EAR)? (Round answer to 2 decimal places)

6.You are evaluating a growing perpetuity investment from a large financial services firm. The investment promises an initial payment of $24,700 at the end of this year and subsequent payments that will grow at a rate of 2.6 percent annually. If you use a 9 percent discount rate for investments like this, what is the present value of this growing perpetuity?(Round answer to 2 decimal places)

7.Cullumber Productions borrowed some money from the California Finance Company at a rate of 13.90 percent for a seven-year period. The loan calls for a payment of $1,253,000 each year beginning today. How much did Cullumber borrow?(Round answer to 2 decimal places)

Answer 1

Sol 1: Susan Wilson IRA balance at the end of 40 years can be find out by using Future Value Annuity Formula: P * ((1+r)^n) - 1)/r here in our case P= 3800 N= Number of Year of Investment 40 and R= Rate of Annual Interest = 8.45% or 0.0845 thus FVIA or IRA Balance at the end of 40 years = $ 11,08,772.75

Sol 2: Donna Clark IRA balance at the end of 65 years can be find out by using Future Value Annuity Formula: P * ((1+r)^n) - 1)/r here in our case P= 2500 N= Number of Year of Investment 41 as she is making payment at the beginning of the year and R= Rate of Annual Interest = 11.00% or 0.11 thus FVIA or IRA Balance at the end of 65 years = $ 16,17,067.33

Sol 3: Kevin Hall require a Sum of $ 5920.00 this can be taken as Future Value Amount in FVIA formula= FV= P * ((1+r)^n) - 1)/r here we need to find the value of P, Rate (R) is 10.5% annually compounded, Time (n) = 3 years thus 5920=P* 3.33 which gives the value of Periodic Payment (P) as = $ 1779.90

Sol 4: In this problem we would use the formula of Present Value Perpetual Annuity = Periodic Income/Rate of Interest in this case Periodic Income = 9600 and ROI= 6.1% or 0.061 if we put the values in the formula we will get $ 157377 which the Grandfather needs to invest to produce the desired cash flow.

Sol 5: Effective Annual Interest Rate = (1+r/no of days in a year)^n*no of days in a year - 1. In this case R= 8.90% No of Days in a Year = 365 N= 1 year thus by computing the values in the formula we get Effective Annual Interest Rate = 9.31% and in value terms $ 1447.22

Sol 6: The formula for Present Value of Growing perpetuity is = Cash flow after first period / difference between discount rate and growth rate. In our case thus Cash flow after first period = 24700; Discount Rate = 9% Growth Rate = 2.6%. By substituting the values in the formula we will get Present Value of Growing Annuity as = $ 385937.50

Sol 7: The borrowing amount of Cullumber Productions can be found out by using PVIAF= P[1-(1+r)^-n/r] here P is the periodic payment which is $ 12,53,000 r = rate of interest = 0.1390; n = term which is 7 years by substituting the values in the formula $ 53,89,704.06 in our case it is mentioned payments are made from beginning of the year we will multiply the Present Value Annuity with (1+r) which is 1.1390 to get $ 61,38,872.90 as our final answer.