Question

3.  Problem 4-31 (Nonannual Compounding)

Nonannual Compounding It is now January 1. You plan to make a total of 5 deposits of $400 each, one every 6 months, with the first payment being made today. The bank pays a nominal interest rate of 8% but uses semiannual compounding. You plan to leave the money in the bank for 10 years. Do not round intermediate calculations. Round your answers to the nearest cent. How much will be in your account after 10 years? $__________________   You must make a payment of $1,924.06 in 10 years. To get the money for this payment, you will make five equal deposits, beginning today and for the following 4 quarters, in a bank that pays a nominal interest rate of 8% with quarterly compounding. How large must each of the five payments be? $__________________

Answer 1

a

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

? = ((1+8/(2*100))^2-1)*100

Effective Annual Rate% = 8.16

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

C = Cash flow per period

i = interest rate

n = number of payments

FV= 400*(((1+ 8.16/200)^(2.5*2)-1)/(8.16/200))*(1+8.16/200)

FV = 2258.5313

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

Future value = 2258.5313*(1+0.0816)^7

Future value = 3911.05

b

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

? = ((1+8/(4*100))^4-1)*100

Effective Annual Rate% = 8.2432

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

1924.06 = Present value*(1+0.082432)^8.5

Present value = 981.326

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

C = Cash flow per period

i = interest rate

n = number of payments

981.326= Cash Flow*(((1+ 8.2432/400)^(1.25*4)-1)/(8.2432/400))*(1+8.2432/400)

Cash Flow = 184.54