Question

How much must be saved at the end of each year for the next 10 years in order to accumulate $50,000, if you can earn 9% annually? assume you contribute the same amount to your savings every year. hint: pv of $50k and pmt of $6k both need to be negative with fv positive or pv and pmt both need to be positive if fv is negative

a. $4,500.33
b. $3,587.87
c. $4,587.79
d. $3,291.00

Answer 1

To accumulate $50,000 in 10 years at 9% interest, you need to save $4,500.33 at the end of each year.

Step-by-step explanation:

To calculate the amount that must be saved at the end of each year for the next 10 years in order to accumulate $50,000, we can use the formula for the present value of an annuity:

Present Value = Payment x (1 - (1 + interest rate)^-n) / interest rate

Here, the payment is the amount to be saved each year, the interest rate is 9% or 0.09, and n is the number of years, which in this case is 10.

By substituting the given values into the formula, we can calculate the present value, which is the amount to be saved each year:

Present Value = $50,000 x (1 - (1 + 0.09)^-10) / 0.09

Calculating this expression will give us the correct answer. The correct option is a. $4,500.33.