Question

Name Chapter 12 Compound Interest and Present Value Part I Vocabulary Matchup A. Twice a year 1. Compound 2. Effective rate (APY B. Stated rate 3. Nominal rate C. D. E. F. Four times per year Amount calculated on adjusted principal 12 times per year Years times number of times compounded in one year True rate of interest Know future amount looking for present Rate divided by number of times compounded per year Periodically interest is calculated and added to 4. Periodts 5. Present value 6. Rate 7. Interest 8. Semiannually 9. Quarterly G. H. L 10. Monthly J. Part II Drill Complete without using tables. (For simplicity, round to nearest cent after each period.) No. of Rato of When Periods to be TotalTotal Principal Time Compound Compounded Compounded Amount Interest $300 1 yr. 6% Quarterly B. C. 12. Solve No. 11 by using compound tables. 12_ Solve by compound table. Total Amount 13, $ 8,000 10% 3years Semiannually. ? 13. 14, $15,000 12% 4years Quarterly- 14.

Answer 1

11. Formula for calculating compound interest

B = P × { 1+ ( r ÷ n ) }^{n × t}

Here, B = Total amount

P = principal amount = $300

r = rate of interest = 6% = 6 ÷ 100 = 0.06

n = number of times per year, interest is compounded = 4

t = time in years = 1 year

A = number of periods to be compounded = 4 (quarterly)

Putting values in formula, we get

B = 300 × { 1 + (0.06 ÷ 4) }^4×1

B = $318.41

C = total interest = total amount - principal = 318.41 - 300 = $18.41

12. Now we have to solve this problem using compound table

compound tableformula for calculating total amount using compound table

B = P × rate factor

We calculate rate factor from the table

In our problem, number of compounding periods = 4

Rate per period = 6% ÷ 4 = 1.5%

Our rate factor is the intersect value of rate per period ( 1.5% ) and number of periods ( 4 ) .

From the table corresponding rate factor = 1.06136

Total amount = B = 300 × 1.06136 = $318.41