Final answer:
The periodic payment needed to obtain $2500 in an account earning 6.5% compounded annually for 4 years is approximately $567.43.
Step-by-step explanation:
To find the periodic payment needed to obtain $2500 in an account earning 6.5% compounded annually for 4 years, we use the formula for the future value of an annuity:
FV = PMT × { [ (1 + r)^n - 1 ] / r }
Where FV is the future value ($2500), PMT is the periodic payment we need to find, r is the interest rate per period (0.065 in decimal form for 6.5%), and n is the total number of periods (4 years).
To find PMT, rearrange the formula to solve for PMT:
PMT = FV / { [ (1 + r)^n - 1 ] / r }
PMT = $2500 / { [ (1 + 0.065)^4 - 1 ] / 0.065 }
PMT = $2500 / { [ (1.065)^4 - 1 ] / 0.065 }
Calculating the values, we get:
PMT = $2500 / { [ (1.2865) - 1 ] / 0.065 }
PMT = $2500 / { (0.2865) / 0.065 }
PMT = $2500 / 4.4077
PMT ≈ $567.43
Therefore, the periodic payment needed to obtain $2500 after 4 years at a 6.5% annual interest rate is approximately $567.43.