Question

A person needs $56000. He/she makes deposits of $1100 at the end of each quarter in an account which earns 10.75% compounded quarterly.

a. How many full deposits are required?

b. Find the amount of the smaller concluding deposit at the end of the next quarter. If no final deposit is required, your answer is 0.

Answer 1

formula of annuity compounded quarterly

FV = C x { (( 1+i)^n) -1} /i

FV = future value = $ 56000

C = cashflow per period = $ 1100

i = quarterly interest rate = 10.75 % quarterly

n = number of quarterly payments = ?  

Solution

FV = C x { (( 1+i)^n) -1} /(i)

56000 = 1100 { ((1.1075)^n } / 0.1075

56000/1100 = 1.1075^n / 0.1075

50.909090 = 1.1075^n / 0.1075

50.909090 x 0.1075 = 1.1075^n

5.47272718 =  1.1075^n

x log 1.1075 = log 5.47272718

x or n = log 5.47272718 / log 1.1075

  = 0.738203798 / 0.044343734

= 16.64730801

Hence 16 full deposites are required

Amount of the smaller concluding deposit at the end of the next quarter is

0.64730801 x 1100 = $712.03880