Question

Your grandfather started his own business 52 years ago. He opened an investment account at the end of his third month of business and contributed $x. Every three months since then, he faithfully saved another $x. His savings account has earned an average rate of 5.73 percent annually. Today, his account is valued at $289,209.11. How much did your grandfather save every three months assuming he saved the same amount each time?

Answer 1

Solution:

Given ,

Grandfather started his own business 52 years ago

Average rate = 5.73

His account is valued at $289,209.11

Now , Calculate How much did your grandfather save every three months assuming he saved the same amount each time

N = 52 *4 = 208

I = 5.73/4 = 1.43

PV = 0

FV = $289,209.11

CPT PMT = $-443.13 ( Using excel )

Answer 2

If my grandfather was saving every three months, the amount he saved each time is $226.78.

Given Information

Future Value = $289,209.11

Annual interest rate = 5.73%

Quarters rate of interest = 5.73/4

Quarters rate of interest = 0.0143

Number of periods = 52 years * 4

Number of periods = 208

PMT = FV / ((1+ i)^n - 1) / i

PMT = $289,209.11 /{ (1+0.014325)^208 -1) / 0.014325}

PMT =$289,209.11 / 1,275.27

PMT = $226.78

In conclusion, If my grandfather was saving every three months, the amount he saved each time is $226.78.

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