To calculate the future value of an annuity, we can use the future value of an annuity formula:
Future Value = Pmt × (((1 + r)^n – 1) / r)
Where:
- Pmt = annuity payment (1,000 in this case)
- r = interest rate per period (8% or 0.08)
- n = number of payments (4 years)
Now, let’s plug in the numbers:
Future Value = 1,000 × (((1 + 0.08)^4 – 1) / 0.08)
Calculating the part within the parenthesis:
- (1 + 0.08) = 1.08
- (1.08)^4 ≈ 1.3605
- (1.3605 – 1) = 0.3605
- Now divide by r (0.08):
- 0.3605 / 0.08 ≈ 4.50625
Putting it all together:
Future Value ≈ 1,000 × 4.50625 ≈ 4,506.25
Therefore, the future value of a 1,000 annuity payment over four years at an 8 percent interest rate is approximately $4,506.25.