Question

To save money for her son's college tuition, Raina invests $101 every month in an annuity that pays 6% interest, compounded monthly. Payments will be made at the end of each month. Find the total value of the annuity in 19 years: bo not round any intermediate computations, and round your final answer to the nearest cent. If necessary, refer to the los of innancial focmulias.

Answer 1

The future value of Raina's annuity, investing $101 monthly at 6% interest compounded monthly for 19 years, is approximately $49,576.86, calculated using the future value formula for annuities.

Step-by-step explanation:

To find the total value of an annuity where monthly contributions are made and interest is compounded monthly, we use the future value of an annuity formula:

FV = P × {[(1 + r)^n - 1] / r}, where:

• FV represents the future value of the annuity,
• P is the periodic payment amount,
• r is the periodic interest rate (annual interest rate divided by the number of periods per year), and
• n is the total number of payments (periods).

In Raina's case, she invests $101 monthly at an interest rate of 6% compounded monthly. Since there are 12 months in a year, the monthly interest rate (r) is 0.06/12. Over 19 years (or 19 × 12 months), the formula becomes:

FV = $101 × {[(1 + 0.005)^228 - 1] / 0.005}

Calculating the value inside the brackets first:

[(1 + 0.005)^228 - 1] ≈ 2.4543

Then multiplying by $101:

FV = $101 × 2.4543 / 0.005 = $101 × 490.86 ≈ $49,576.86

Therefore, the total value of the annuity after 19 years is approximately $49,576.86, rounded to the nearest cent.