Question

Please complete the following time value of money questions. You must show your calculations and you must use the TABLES to do those calculations (thus, you must show the factor that you have used from the table when documenting how you arrived at your answer, and you must use the factors as they are shown in the tables. Do not round them). However, please round your final answers to two decimal places (i.e., show dollars and cents).

1. You win a sweepstakes and receive $50,000. If you invest the money in an interest-earning bank account that pays 8% interest, compounded quarterly, how much will this gift be worth after 10 years?

2. You are starting to give your favorite charity a yearly gift, such that you will need to withdraw $10,000 a year from your interest-earning bank account. You expect you will be giving the charity this yearly gift for 10 years and for your bank account to earn 7%, compounded annually. How much money do you need in the account today in order to make these withdrawals?

3. 6 years from now, you will receive a $600,000 gift from your grandpa. If the current interest rate is 6%, what is the value of this amount in today’s dollars assuming that interest is compounded semiannually? In other words, how much does your grandpa need to have today to make sure that he can give you the $600,000 6 years from now

Answer 1

1) Given information

Principal amount (p) = $50,000

Interest (I) = 8%

Time period (n) = 10years compounded quaterly

Future value = p (1+i)n

= 50,000(1+8/100*4)10*4

= 50,000( 1+0.02) whole power 40

= 50,000*1.02 whole power 40

=50,000*2.20804

= $110,402

2 ) Given information

Withdrawal amount = 10,000

10years, interest = 7%

Formula : PVAn = R ( PVIF i,n )

= 10,000*7.024 ( in the present value (ordinary) annuity table for 10 years 7%interest value is 7.024)

PVAn = 70240

3) Given

Future value = 600,000

i= 6% , n = 6years ; compounded semiannually

Present value = F/ (1+i) whole power n

600,000/ ( 1+ 6/100*2) whole power 6*2

= 600,000/ (1+0.03) 12

= 600,000/ (1.03) whole power 12

= 600,000/1.4258

= 420,816