Question

Suppose you have $2000 to invest in an account and aim to reach $2500 in one year. What interest rate would you need if the amount is compounded monthly? Round your answer to the nearest percent.

Options:
A. 15%
B. 20%
C. 25%
D. 30%

Answer 1

To find the interest rate needed to reach $2500 in one year with monthly compounded interest, use the formula A = P(1 + r/n)^(nt). Substituting the values, the interest rate is approximately 19.2%.

Step-by-step explanation:

To find the interest rate needed to reach $2500 in one year with a monthly compounded interest, we can use the formula:

A = P(1 + r/n)^(nt)

Where:

• A is the future value we want to reach ($2500)
• P is the present value we have ($2000)
• r is the interest rate we are trying to find
• n is the number of times interest is compounded per year (12 for monthly compounded interest)
• t is the number of years (1 year)

Substituting the values into the formula, we get:

2500 = 2000(1 + r/12)^(12(1))

Simplifying the equation, we get:

1.25 = (1 + r/12)^12

To solve for r, we take the twelfth root of both sides and subtract 1:

r/12 = 0.251/12 - 1

r ≈ (0.251/12 - 1) * 12

r ≈ 0.192

So, the interest rate needed to reach $2500 in one year with monthly compounded interest is approximately 19.2%.