You have an investment account that started with $3 comma 000 10 years ago and which now has grown to $6 comma 000. a. What annual rate of return have you earned (you have made no additional contributions to the account)? b. If the investment account earns 15 % per year from now on, what will the account's value be 10 years from now?

The correct answer for option (a) is 7.17% and for option (b) is $48,546.69.

Explanation:

According to the scenario, the given data are as follows:

(a) Present value = $3,000

Future value = $6,000

Time period = 10 years

So, we can calculate the annual rate of return by using following formula:

Rate of return = (( FV ÷ PV)^1/t  -1)

= (( $6,000 ÷ $3,000)^1/10 -1)

= (2)^0.1 - 1

= 1.07177346254 - 1

= .07177 or 7.17%

(b) Present value = $12,000

Rate of interest (r) = 15%

Time period = 10 year

So, we can calculate the Future value by using following formula:

FV = PV × ( 1+r)^t

= $12,000 × ( 1 + 15%)^10

= $12,000 × 4.04555773571

= $48,546.69