How much money must you pay into an account at the beginning of each of 20 years in order to have $10,000 at the end of the 20th year? Assume that the account pays 12% per year,and round to the nearest $1.
A) $1,195
B) $111
C) $124
D) $139

Question

Quizplus · Accepted Answer

This problem involves finding the present value of a future sum. We can use the formula:

PV = FV / (1 + r)^n

where PV is the present value, FV is the future value, r is the interest rate per period, and n is the number of periods.

In this case, we want to find how much we need to pay into the account each year (the present value) in order to have $10,000 at the end of 20 years (the future value), given an interest rate of 12% per year (r).

We can rearrange the formula to solve for PV:

PV = FV / (1 + r)^n

PV = $10,000 / (1 + 0.12)^20

PV = $1,195.68

So we would need to pay $1,195.68 into the account at the beginning of each year to have $10,000 at the end of the 20th year. However, we are asked to round to the nearest dollar, so the answer is $1,196.

Now, we need to determine the closest answer choice. The only answer choice within $1 of $1,196 is C) $124. By paying $124 at the beginning of each year for 20 years, we would have:

PV = $124 x [1 - (1 + 0.12)^-20] / 0.12
PV = $124 x 8.559
PV = $1,063.22

This is less than the required present value of $1,195.68, which means that option C is not enough. The next closest answer choice is D) $139. By paying $139 at the beginning of each year for 20 years, we would have:

PV = $139 x [1 - (1 + 0.12)^-20] / 0.12
PV = $139 x 8.559
PV = $1,190.60

This is within $1 of the required present value of $1,195.68, which means that option D) $139 is the best choice.

How Much Money Must You Pay into an Account at the Beginning