Given below are the future value factors for 1 at 8% for one to five periods. Each of the items 48 to 51 is based on 8% interest compounded annually.

-What amount should be deposited in a bank account today to grow to $10,000 three years from today?
A)$10,000 × 1.260
B)$10,000 × 1.260 × 3
C)$10,000 ÷ 1.260
D)$10,000 ÷ 1.080 × 3

Question

Given below are the future value factors for 1 at 8% for one to five periods. Each of the items 48 to 51 is based on 8% interest compounded annually.

-What amount should be deposited in a bank account today to grow to $10,000 three years from today?
A)$10,000 × 1.260 
B)$10,000 × 1.260 × 3 
C)$10,000 ÷ 1.260 
D)$10,000 ÷ 1.080 × 3

Quizplus · Accepted Answer

We can use the formula for present value of a lump sum: 
PV = FV / (1 + r)^n 
where PV is present value, FV is future value, r is the annual interest rate, and n is the number of years. 
Plugging in the given values: 
PV = 10,000 / (1 + r)^3 
We don't know the interest rate, so we can't solve for PV. However, we are given answer choices that involve calculations with the interest rate. 
Choice A multiplies the future value by 1.260, which implies that the interest rate is 26%. This is an unrealistic and unlikely interest rate, so we can eliminate this choice. 
Choice B multiplies the future value by 1.260 and by 3, which implies that the interest rate is 26% per year for 3 years. Again, this is an unrealistic and unlikely interest rate, so we can eliminate this choice. 
Choice C divides the future value by 1.260, which implies that the interest rate is 26% per year. This is a high but possible interest rate, so we can keep this choice. 
Choice D divides the future value by 1.080 and multiplies by 3, which implies that the interest rate is 8% per year for 3 years. This interest rate is more realistic than the choices involving 26%, but it still seems low for a bank deposit. 
Therefore, the best choice is C, which gives a present value of approximately $7,936.51 when rounded to the nearest cent.

Given Below Are the Future Value Factors for 1 at 8