Question

What interest rate must your bank offer if you want your $2.730 invested today to grow to $3,470

in 3 years? Round to two places past the decimal point.
a. 8.32%
b. 11.56 %
c. 6.95%
d. 7.52%

Answer 1

To determine the required interest rate, the compound interest formula is used. An interest rate of approximately 8.3%, or precisely 8.32% rounded to two decimal places, is required for $2,730 to grow to $3,470 in 3 years.

Step-by-step explanation:

The question is asking for the interest rate needed for an investment of $2,730 to grow to $3,470 in 3 years. To find this, we can use the compound interest formula:

A = P(1 + r)^n

where:

• A is the amount of money accumulated after n years, including interest.
• P is the principal amount (the initial amount of money).
• r is the annual interest rate (decimal).
• n is the number of years the money is invested.

Using the given values, solve the equation for r:

$3,470 = $2,730(1 + r)^3

Divide both sides by $2,730:

1.271 r ≈ (1 + r)^3

Now, take the cube root of both sides to solve for r:

(1 + r) ≈ 1.083 (after rounding to three decimal places)

Subtract 1 from both sides and convert to percentage:

r ≈ 0.083 or 8.3%

Rounding off to two decimal places, we find that the interest rate required is 8.32%, which corresponds to option (a).