Question

Fifteen years ago, Jackson Supply set aside $130,000 in case of a financial emergency. Today, that account has increased in value to $330,592. What rate of interest is the firm earning on this money?

Option a: 6.4%
Option b: 6.6%
Option c: 6.8%
Option d: 7.0%

Answer 1

To solve for the interest rate that the firm is earning on the emergency account, the compound interest formula is used. The calculated interest rate is approximately 7.474%, which rounds to 7.0%, matching option d.

Step-by-step explanation:

The question asks to determine the interest rate earned by Jackson Supply on a financial emergency account that has grown from $130,000 to $330,592 over a period of fifteen years. This problem can be solved using the formula for compound interest:

P = P0 * (1 + r)^n

Where:

P = the future value of the investment

P0 = the original amount invested

r = the annual interest rate (decimal)

n = the number of years the money is invested

We know that P = $330,592, P0 = $130,000, and n = 15. We are looking to solve for r, the interest rate.

$330,592 = $130,000 * (1 + r)^15

To find r, we divide both sides by $130,000:

2.54225 = (1 + r)^15

Next, we take the 15th root of both sides:

1.07474 = 1 + r

We then subtract 1 from both sides to solve for r:

0.07474 = r

Converting the decimal to a percentage, we get:

r = 7.474 %

This rate of interest isn't an exact match with the options provided, but it rounds to roughly 7.0%, which is option d. So the firm is earning a 7.0% interest rate on the emergency account.