Question

You put $125.32 at the end of each month in an investment plan that pays 2.5% interest, compounded monthly. How much will you have after 23 years? Round to the nearest cent.

a).$46,683.28
b) $46,700.15
c) $46,665.42
d) $46,698.79

Answer 1

The question is based on calculating the future value of monthly investments using the formula for an annuity with compound interest. To find the total amount after 23 years, values need to be plugged into the formula that accounts for monthly payments, monthly interest rate, and total number of payments. Compound interest significantly boosts the growth of an investment over time.

Step-by-step explanation:

The subject of this question is Mathematics, and it involves calculating the future value of a series of equal monthly payments in an investment that pays out compound interest. We can find the answer using the future value formula for an annuity with compound interest:
FV = P × `((1 + r)^n - 1) / r`

Where:

• FV is the future value of the investment
• P is the monthly investment amount ($125.32)
• r is the monthly interest rate (2.5% per year or 0.025 / 12 per month)
• n is the total number of payments (23 years × 12 months/year)

To find out the total amount after 23 years, we need to plug these values into the formula and calculate the sum.

Compound interest is powerful because the interest earned is reinvested, earning more interest over time, leading to exponential growth in the investment. The longer the time period, the more substantial the effect of compound interest, as illustrated by the analogy of the bank account at 2% annual interest in Box 1.2. Similarly, starting early as pointed by the case of a $3,000 investment growing nearly fifteen fold in 40 years demonstrates the essence of compound interest.