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