Question

What is the size of the payment that must be deposited at the beginning of each quarter in an account that pays 4.2% compounded quarterly, so that the account will have a future value of $111,000.00 at the end of 14 years?
The quarterly payments are $________. (Round to 2 decimal places.)

Answer 1

Given

Interest rate = 4.2% Compounding Quarterly

Interest rate per Quarter = 4.2% /4 = 1.05%

Future Value = $ 111000

No.of Years = 14 Years

No.of Quartely paymennts in 14 Years = 14*4 = 56

We know that Future value of Annuity due = C[ {( 1+i)^n - 1}/I ] ( 1+i)

Here C = Cash flow per period

i = Interest rate per period

n = No. of Payments

Future value of Annuity due = C[ {( 1+i)^n - 1}/I ] ( 1+i)

$ 111000 = C [ { 1+0.0105)^56 - 1} / 0.0105] ( 1+0.0105)

$ 111000 = C [ {1.0105}^56 - 1} / 0.0105] ( 1.0105)

$ 111000 = C [ {1.7949-1}/0.0105] ( 1.0105)

$ 111000 = C [ { 0.7949}/0.0105 ] ( 1.0105)

$ 111000 = C [ 75.70476] ( 1.0105)

$ 111000/ ( 75.70476) ( 1.0105) = C

$ 111000/ 76.49966 = C

$ 1450.99 = C

The Quartely Payments are $ 1450.99