Your big brother deposited $10,000 today at 9% interest for 6 years. You would like to have just as much money at the end of the next 6 years as your brother. However, you can only earn 7.5% interest. How much more money must you deposit today than your brother did if you are to have the same amount at the end of the 6 years?
A) $398.68
B) $487.63
C) $575.00
D) $648.21
E) $866.96

Question

Quizplus · Accepted Answer

To solve this problem, we need to calculate the future value of both deposits and then find the difference in the present value required to achieve the same future value at different interest rates.First, calculate the future value of the brother's deposit using the formula for future value: FV = PV * (1 + r)^n, where PV is the present value, r is the annual interest rate, and n is the number of years.For the brother's deposit:PV = $10,000r = 9% or 0.09n = 6 yearsFV = $10,000 * (1 + 0.09)^6 ≈ $16,093.71Next, we need to find out how much you need to deposit to have the same amount in 6 years at a 7.5% interest rate. We already know the future value we want to achieve ($16,093.71), so we rearrange the future value formula to solve for the present value (PV):PV = FV / (1 + r)^nFor your deposit:FV = $16,093.71 (the target future value)r = 7.5% or 0.075n = 6 yearsPV = $16,093.71 / (1 + 0.075)^6 ≈ $10,866.96Finally, to find out how much more you need to deposit than your brother, subtract your brother's initial deposit from your required deposit:$10,866.96 - $10,000 = $866.96Therefore, you must deposit $866.96 more than your brother to have the same amount at the end of 6 years.

Your Big Brother Deposited $10,000 Today at 9% Interest for 6