Tony Hippwaist wants to have $966,793 in his savings account in six years. Tony

Question

 Tony Hippwaist wants to have $966,793 in his savings account in six years. Tony opened his savings account by
depositing $10,000. Tony intends to make equal deposits at the beginning of every three months for the next
six years. Tony will earn 20% interest compounded quarterly on all deposits with the bank. 

 Calculate the amount of each equal quarterly deposit that Tony must make in order to have $966,793 in his
account in six years. 

 Please include work so that I can follow your reasoning. Thank you! 

Explanation / Answer

Quarterly interest rate = annual rate / 4 = 20%/4 = 5%

There are 2 ways of solving this problem.

Solution 1 - using annuity due formula:

Tony will make his first deposit today and then subsequent deposits every 3 months for the next 6 years. So total number of payments = 6*4 = 24 payments

Let him make payment of $X every 3 months.

Future value of the opening $ 10,000 = 10,000*(1+quarterly interest rate)^24 = 10,000*1.05^24 = 32,251

Future value of the remaining 24 payments = X * ((1+5%)^23-1) / 5% * (1+5%) = 46.7271 * X

So total future value = 32,251 + 46.7271 * X

This is equal to 966,793

So 32,251 + 46.7271 * X = 966,793

Solving, we get X = $ 20,000

Solution 2 - using Excel formula

We can use the PMT function in Excel as follows:

Punch in =PMT(5%,24,10000,-966793,1), where:

first parameter is quarterly interest rate

second parameter is number of payments

third parameter is initial payment of 10000

fourth parameter is future value of 966793

last parameter is indicating annuity due

This is equal to $ 20,000.

So we can use either method to find the answer of 20,000.

Hope this helped ! Let me know in case of any queries.

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