Question

Suppose you invest $130 a month for 3 years into an account earning 8% compounded monthly. After 3 years, you leave the money, without making additional deposits, in the account for another 21 years. How much will you have in the end?

A) $50,000

B) $75,000

C) $100,000

D) $125,000

Answer 1

The amount at the end is D) $125,000

Step-by-step explanation:

Compounding interest is a powerful tool for wealth accumulation. In this scenario, investing $130 monthly at an 8% interest rate compounded monthly for the initial 3 years sets the foundation for significant growth. After the initial investment period, the money continues to accrue interest for an additional 21 years.

The formula for compound interest is A = P
`(1 + r/n)^(^n^t^)`, where A is the future value, P is the principal (initial investment), r is the annual interest rate, n is the number of times interest is compounded per year, and t is the time in years. In this case, A = 130
`(1 + 0.08/12)^(^1^2^ *^ 3^)` calculates the value after the initial 3 years, and subsequently, A = A
`(1 + 0.08/12)^(^1^2^ *^ 2^1^)` gives the final amount after the additional 21 years. The result is approximately $125,000, making option D the correct answer.

In the first 3 years, the investment grows significantly due to the monthly compounding of interest, and the power of compounding continues to work over the subsequent 21 years, further multiplying the wealth. The compounding frequency, monthly in this case, plays a crucial role in enhancing the overall returns. It is this compounding effect that leads to the substantial increase in the final amount. Thus, diligent monthly contributions coupled with the compounding factor contribute to the final balance of $125,000.

In conclusion, the correct answer is $125,000 (option D), and the substantial growth is a testament to the compounding effect, emphasizing the importance of regular contributions and the time value of money in long-term investment strategies.