Question

" O Consumer Mathematics Finding the periodic payment needed to meet an investment goal To help out with her retirement savings, Salma invests in an ordinary annuity that earns 4.2% interest, compounded monthly. Payments will be mad of each month. 0 How much money does she need to pay into the annuity each month for the annuity to have a total value of $98,000 after 18 years? Do not round intermediate computations, and round your final answer to the nearest cent. If necessary, refer to the list of financial formulas. $ Explanation Check 2023 McGraw Hill LLC. All Rights Reserved. Terms of Use I​

Answer 1

Salma needs to pay approximately $263.36 into the annuity each month to have a total value of $98,000 after 18 years.

Step-by-step explanation:

To calculate the periodic payment needed to meet an investment goal, we can use the formula for the future value of an ordinary annuity:

V = P * ((1 + r/n)^(n*t) - 1) / (r/n)

Where:

• V is the future value
• P is the periodic payment
• r is the interest rate
• n is the number of compounding periods per year
• t is the number of years

In this case, the future value (V) is $98,000, the interest rate (r) is 4.2% or 0.042, the number of compounding periods per year (n) is 12 (monthly compounding), and the number of years (t) is 18.

1. Substitute these values into the formula: 98000 = P * ((1 + 0.042/12)^(12*18) - 1) / (0.042/12)
2. Simplify the formula: 98000 = P * (1.0035^(216) - 1) / 0.0035
3. Calculate the expression in the parentheses: 1.0035^216 ≈ 2.301
4. Rewrite the equation: 98000 = P * (2.301 - 1) / 0.0035
5. Simplify further: 98000 = P * 1.301/0.0035
6. Multiply both sides of the equation by 0.0035: P ≈ 98000 * 0.0035 / 1.301
7. Calculate the result: P ≈ $263.36

Therefore, Salma needs to pay approximately $263.36 into the annuity each month to have a total value of $98,000 after 18 years.