Spencer Corporation will invest $20,000 every December 31st for the next six years (2014 - 2019). If Spencer will earn 12% on the investment, what amount will be in the investment fund on December 31, 2019?

Question

Quizplus · Accepted Answer

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

FV = PMT x (((1 + r)^n - 1) / r)

Where:
PMT = the amount invested every year
r = the interest rate per period (in this case, per year)
n = the number of periods (in this case, 6 years)

Plugging in the values given in the problem, we get:

FV = 20,000 x (((1 + 0.12)^6 - 1) / 0.12)
FV = 20,000 x (2.0123)
FV = $40,246

This is the amount that will be in the investment fund on December 31, 2019 if only the $20,000 invested each year is considered. However, we also need to add the interest earned on the investment over the six years. This can be done using the same formula, but with the beginning balance as the present value:

FV = PV x (1 + r)^n

Where:
PV = the beginning balance (which is the same as the $20,000 invested on December 31, 2014)
r = the interest rate per period (in this case, per year)
n = the number of periods (in this case, 6 years)

Plugging in the values, we get:

FV = 20,000 x (1 + 0.12)^6
FV = $39,058

Adding this to the $40,246 from the annual investments, we get a total future value of:

FV = $40,246 + $39,058
FV = $79,304

However, the question asks for the amount on December 31, 2019, which means we need to compound the interest one more time for a total of 7 years. Using the same formula with a beginning balance of $79,304 and a 12% interest rate, we get:

FV = 79,304 x (1 + 0.12)^1
FV = $88,802

Therefore, the best choice is C, $162,304.

Spencer Corporation Will Invest $20,000 Every December 31st for the Next