To pay for her college education, Gina is saving $2,000 at the beginning of each year for the next eight years in a bank account paying 12 percent interest. How much will Gina have in that account at the end of 8th year?

Question

Quizplus · Accepted Answer

We can use the formula for the future value of an annuity:

FV = Pmt x [(1 + i)^n - 1] / i

Where:
Pmt = Payment per period
i = Interest rate per period
n = Number of periods

In this case, Pmt = $2,000, i = 12% / 12 = 1% per month, and n = 8 years x 12 months/year = 96 months.

Plugging in the numbers, we get:

FV = $2,000 x [(1 + 0.01)^96 - 1] / 0.01
FV = $2,000 x [2.7183^0.01^96 - 1] / 0.01
FV = $2,000 x [3.1214 - 1] / 0.01
FV = $2,000 x 212.14
FV = $425,552

Therefore, Gina will have $425,552 in her account at the end of the 8th year. However, since the question asks for the amount at the end of the 8th year specifically, we need to multiply this by (1 + 0.01)^12 to account for the interest earned during that year:

FV = $425,552 x (1 + 0.01)^12
FV = $425,552 x 1.1268
FV = $479,626

Rounding to the nearest dollar gives us:

FV = $479,626

Therefore, the best choice is D: $27,552.

To Pay for Her College Education, Gina Is Saving $2,000