Question

An account invested in a money market fund grew from $73,364.34 to $73,664.58 in a month. What was the interest rate to the nearest tenth? What was the interest rate?

(Do not round until the final answer. Then round to the nearest tenth as needed.)

Answer 1

4.9%

Explanation:

You want the interest rate that grows $73,364.34 to $73,664.58 in a month.

Account value

The value of an account earning simple interest is ...

A = P(1 +rt)

where P is the amount invested, r is the annual interest rate, and t is the number of year.

Rate

Here, we want to find r.

A/P = 1 +rt . . . . . divide by P

(A/P -1) = rt . . . . subtract 1

(A/P -1)/t = r . . . . divide by the time period in years

Using the given values, we have ...

r = (73664.58/73364.34 -1)/(1/12) ≈ 0.049109 ≈ 4.9%

The interest rate on the account was about 4.9%.

__

Additional comment

Interest earned is "simple interest" up until the point in time that it is folded into the principal (capitalized). Usually, that is no more often than once a month.

<95141404393>