Sol's Laundry began depositing $1, 000 equal annual deposits in a fund beginning on January 2, 2010.The fund earns 10% compounded annually, and the last deposit is made on January 2, 2014.How much will be in the fund on January 2, 2015, one year after the final deposit?
A)$7, 500
B)$6, 716
C)$6, 105
D)$5, 641

Question

Quizplus · Accepted Answer

To solve this problem, we need to use the formula for the future value of an annuity:

FV = Pmt x {[(1 + r)^n - 1] / r}

where:
Pmt = the equal annual deposit
r = the annual interest rate
n = the number of periods (in this case, the number of deposits)

Plugging in the given values, we get:

FV = $1,000 x {[(1 + 0.10)^4 - 1] / 0.10}
FV = $1,000 x {[(1.10)^4 - 1] / 0.10}
FV = $1,000 x 4.641
FV = $4,641

This is the value of the fund on January 2, 2014, immediately after the final deposit. To find the value one year later, we simply compound the interest for one more year:

FV = $4,641 x 1.10
FV = $5,105.10

Therefore, the answer is B) $6,716.

However, the answer choices given in the question do not match the correct answer. The closest answer choice is C) $6,105, which is only off by a few dollars.

Sol's Laundry Began Depositing $1, 000 Equal Annual Deposits in a Fund