Question

Problem 4-31
Non Annual Compounding

It is now January 1. You plan to make a total of 5 deposits of $500 each, one every 6 months, with the first payment being made today. The bank pays a nominal interest rate of 10% but uses semiannual compounding. You plan to leave the money in the bank for 10 years.

1. How much will be in your account after 10 years? Round your answer to the nearest cent.
   $  
   
2. You must make a payment of $1,658.29 in 10 years. To get the money for this payment, you will make 5 equal deposits, beginning today and for the following 4 quarters, in a bank that pays a nominal interest rate of 14% with quarterly compounding. How large must each of the 5 payments be? Round your answer to the nearest cent.
   $  

Answer 1

a

FVAnnuity Due = c*(((1+ i)^n - 1)/i)*(1 + i )

C = Cash flow per period

i = interest rate

n = number of payments

FV= 500*(((1+ 10/200)^(2.5*2)-1)/(10/200))*(1+10/200)

FV = 2900.96

EAR = [(1 +stated rate/no. of compounding periods) ^no. of compounding periods - 1]* 100

? = ((1+10/(2*100))^2-1)*100

Effective Annual Rate% = 10.25

Future value = present value*(1+ rate)^time

Future value = 2900.96*(1+0.1025)^7.5

Future value = 6030.89

b

EAR = [(1 +stated rate/no. of compounding periods) ^no. of compounding periods - 1]* 100

? = ((1+14/(4*100))^4-1)*100

Effective Annual Rate% = 14.7523

Future value = present value*(1+ rate)^time

1658.29 = Present value*(1+0.147523)^8.75

Present value = 497.4486

FVAnnuity Due = c*(((1+ i)^n - 1)/i)*(1 + i )

C = Cash flow per period

i = interest rate

n = number of payments

497.4486= Cash Flow*(((1+ 14/400)^(1.25*4)-1)/(14/400))*(1+14/400)

Cash Flow = 89.63