Business Mathematics Brief 12th Edition by Stanley Salzman ,Gary Clendenen, Charles Miller

Exercise 20

Use the formula for compound amount, not the table, to find the compound amount and interest. Round to the nearest cent. (See Examples.)
Finding the Interest Rate per Compounding Period and the
Number of Compounding Periods
Find the interest rate per compounding period and the number of compounding periods for each.
(a) 5% compounded semiannually, 3 years
(b) 6% per year, compounded monthly,
years
(c) 2% per year, compounded quarterly, 5 years
SOLUTION
(a) 5% compounded semiannually is
credited at the end of each 6 months. There are 3 years ×2 periods per year = 6 compounding periods in 3 years.
(b) 6% per year, compounded monthly, results in
credited at the end of each month. There are 2.5 years ×12 periods per year = 30 compounding periods in 2.5 years.
(c) 2% per year, compounded quarterly, results in
credited at the end of each quarter. There are 5 years ×4 periods per year = 20 compounding periods in 5 years.
Finding Compound Interest
An investment managed by Bank of America pays 7, interest per year compounded semian-nually. Given an initial deposit of $4500, (a) use the formula to find the compound amount after 5 years, and (b) find the compound interest.
SOLUTION
(a) Interest is compounded at
every 6 months for 5 years × 2 periods per year = 10 periods. Therefore, 3.5% is the interest rate per compounding period ( i ) and 10 is the number of compounding periods ( n ).

The compound amount is $6347.69.
(b)

The interest is $1847.69.
The calculator solution for part (a) is as follows.

Note: Refer to Appendix B for calculator basics.