Question

Assuming a 7% (0.07) Interest rate, $200 invested today in a savings account today will be worth $214 in one year. What will that amount be in 2 and 3 years, and what is the total interest you will earn at the end of three years?

A. In 2 years: $228, In 3 years: $242, Total Interest: $42
B. In 2 years: $216, In 3 years: $230, Total Interest: $30
C. In 2 years: $224, In 3 years: $238, Total Interest: $38
D. In 2 years: $220, In 3 years: $234, Total Interest: $34

Answer 1

The future value of $200 invested at a 7% interest rate is $228 after two years and $245 after three years using compound interest. None of the options provided are correct; the total interest earned at the end of three years is $45.

Step-by-step explanation:

Calculating the future value of an investment using a compound interest can be done through the formula A = P(1 + r)^n, where A is the amount of money accumulated after n years, including interest, P is the principal amount (initial investment), r is the annual interest rate (decimal), and n is the number of years the money is invested.

Using this formula, $200 invested at a 7% interest rate for one year grows to $214, as given. Now, to find out how much the money will be worth in two and three years, we apply the compound interest formula:

1. In two years: $200 × (1 + 0.07)^2 = $200 × 1.1449 = $228.98, which rounds down to $228.
2. In three years: $200 × (1 + 0.07)^3 = $200 × 1.2250 = $245.00, which rounds down to $245.

The total interest earned at the end of three years is the final amount minus the original principal, which is $245 - $200 = $45. Therefore, none of the given options (A, B, C, or D) are correct. The correct amounts are: In 2 years: $228, In 3 years: $245, and Total Interest: $45.