Question

You just found out that you have $1,307.17 in a savings account. Your uncle opened the account in your name exactly 6 years ago, and deposited $X in the account. Then he put in another $240 three years after opening the account. Other than $X and the $240, there were no other deposits. If the interest rate for the past 6 years has been 6%, what is X?

Answer 1

Amount in the account (FV) = $1,307.17

This is equivalent to X(F/P, 6%, 6) + 240(F/P, 6%, 3)

We then have

$1,307.17 = X(F/P, 6%, 6) + 240(F/P, 6%, 3)

1307.17 = X*1.06^6 + 240*1.06^3

X = (1307.17 - 240*1.06^3)/1.06^6

= 720

Hence the value of X is 720