Use a calculator to evaluate an ordinary annuity formula
A = m
1 +
r
n
nt
− 1
r
n
for m, r, and t (respectively). Assume monthly payments. (Round your answer to the nearest cent.)
$150; 5%; 40 yr
A = $
To evaluate the ordinary annuity formula A = m(1 + r/n)^(nt) - 1/(r/n) for the given values, follow these steps:
Step 1: Convert the interest rate from a percentage to a decimal.
5% = 0.05
Step 2: Convert the number of years to the number of months.
40 years = 40 * 12 = 480 months
Step 3: Substitute the values into the annuity formula:
A = $150(1 + 0.05/12)^(12*40) - 1/(0.05/12)
Step 4: Simplify the formula.
A = $150(1 + 0.0041667)^(480) - 1/(0.0041667)
A = $150(1.0041667)^(480) - 1/(0.0041667)
Step 5: Use a calculator to evaluate the expression.
A ≈ $236,013.10
Therefore, A is approximately $236,013.10.
To evaluate the ordinary annuity formula for the given values, follow these steps:
1. Write down the formula: A = m * ((1 + (r/n))^(n*t) - 1) / (r/n)
2. Plug in the values: m = $150, r = 5%, t = 40 years
3. Convert the annual interest rate to a monthly interest rate: r = 5% / 12 = 0.4167%
4. Convert the time period to the number of months: t = 40 years * 12 = 480 months
5. Plug in the values into the formula:
A = $150 * ((1 + (0.4167%/12))^(12*480) - 1) / (0.4167%/12)
6. Perform the calculations within parentheses:
A = $150 * ((1 + (0.0347))^(5760) - 1) / (0.0347)
7. Raise (1 + 0.0347) to the power of 5760 and subtract 1:
A = $150 * ((1.0347)^(5760) - 1) / (0.0347)
8. Calculate (1.0347)^(5760) and subtract 1:
A = $150 * (2210.2771 - 1) / (0.0347)
9. Subtract 1 from 2210.2771:
A = $150 * 2209.2771 / (0.0347)
10. Divide $150 by 0.0347:
A = $150 * 2209.2771 / 0.0347
11. Perform the final calculation:
A = $4,816,565.68
Therefore, A is equal to $4,816,565.68.