To calculate the future value of an annuity, we can use the future value of an annuity formula:
FV = Pmt ×
((1 + r)^nt – 1) / r
Where:
- FV is the future value of the annuity.
- Pmt is the payment amount per period.
- r is the interest rate per period.
- nt is the total number of payments.
In our case:
- Pmt = $1,000
- Annual interest rate = 12%, so the quarterly rate (r) = 12% / 4 = 3% = 0.03
- Number of years = 10, so total periods (nt) = 10 years × 4 quarters/year = 40 quarters
Now we can substitute values into the formula:
FV = 1000 × ((1 + 0.03)^(40) – 1) / 0.03
Calculating this:
- (1 + 0.03)^(40) = 3.262
- So, FV = 1000 × ((3.262 – 1) / 0.03)
- FV = 1000 × (2.262 / 0.03) = 1000 × 75.4 = 75,401
Therefore, the future value of the annuity is approximately $75,401, which corresponds to option d.