Determine the amount of money in a savings account at the end of 3 years, given an initial deposit of $9,000 and an annual interest rate of 4 percent when interest is compounded:

Use Appendix Afor an approximate answer, but calculate your final answer using the formula and financial calculator methods. (Do not round intermediate calculations. Round your final answers to 2 decimal places.) Future value:

a. Annually

b. Semiannually

c. Quarterly

The correct answer for option (a) is $10,124, option (b) is $10,135 and option (c) is $10,141.

Explanation:

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

Initial amount (p) = $9,000

Annual interest rate (r1) = 4%

Semi annual interest rate (r2) = 4% / 2 = 2%

Quarterly interest rate (r3) = 4% / 4 = 1%

Time period (annual) (n1) = 3 years = 3

Time period (semi-annual) (n2) = 3 * 2 = 6

Time period (quarterly) (n3) = 3 * 4 = 12

So, we can calculate future value by using following formula:

A = P (1 + r) ^n

(a). Putting the value in the formula

A = P (1 + r1) ^n1

= $9,000 (1 + 4%) ^3

= $9,000 x (1.04) ^3

= $10,124

(b). Putting the value in the formula

A = P (1 + r2) ^n2

= $9,000 (1 + 2%) ^6

= $9,000 x (1.02) ^6

= $10,135

(c.) Putting the value in the formula

A = P (1 + r3) ^n3

= $9,000 (1 + 1%) ^12

= $9,000 x (1.01) ^12

= $10,141