The Mathematics of Money

C. Using Effective Rates for Comparisons

Find the effective rate equivalent to each of the three rates in question 5. Which of the effective rates is lowest? Does
this agree with your answer to question 5?

Find the effective rate equivalent to each of the rates given in the table below, and use them to decide which rate is
actually the highest and which is actually the lowest.

Bank Rate Compounding

First National Bank Second National Bank Third National Bank Fourth National Bank Fif th National Bank

8.81%

8.99%

9.12%

8.84%

9.04%

Daily Quarterly Annually Monthly Annually

Which of the following fi nancial institutions is offering the most attractive rate for personal loans?

Bank Rate APR

Bank of Newark Port Gibson Financial Seneca Castle Savings

10.95%

11.15%

10.99%

11.57%

11.74%

11.56%

Which of the following fi nancial institutions is offering the most attractive rate for certifi cates of deposit?

Bank Rate APY

Perinton Trust Penfi eld Mutual Pittsford Savings Bank

3.97% compounded daily 4.19% compounded annually 4.06% compounded monthly

4.05%

4.19%

4.14%

D. Using Effective Rates in Calculations

Emma put $1,209.35 into a 4-year CD. The effective interest rate for her account was 3.99%. How much will her CD
be worth when it matures?

Javier invested $2,881 at an effective interest rate of 7.25% for 2 years. How much interest did he earn?

If you can earn an effective rate of 7.29% on an investment, how much would you need to invest in order to have
$1,000 in 3 years?

Toby’s bank compounds interest daily in his account. If the effective interest rate is a constant 6.02%, how much will
$750 grow to in 5 years?

124 Chapter 3 Compound Interest