We can use the formula for compound interest:
A = P(1 + r/n)^(nt)
where A is the future value, P is the present value (or principal), r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the number of years.
In this case, we want to find P, so we can rearrange the formula:
P = A/(1 + r/n)^(nt)
Plugging in the values we have:
A = $32,000
r = 6.4% = 0.064 (decimal)
n = 4 (compounded quarterly)
t = 5 years
P = 32000/(1 + 0.064/4)^(4*5)
P = $24,358.19
Therefore, Gordon should deposit $24,358.19 today in order to have $32,000 in 5 years, assuming he earns 6.4% interest compounded quarterly.
Gordon Freeman wants to have $32,000 in 5 years in order to purchase a new car.
(a) How much should he deposit today in an account earning 6.4%, compounded quarterly,
to have the required amount in 5 years?
1 answer
1 answer