C. Comparing Compounding Frequencies
- Complete the following table comparing the future value of $1,600 at 9% interest in 20 years, using different
compounding frequencies.
Frequency Times/Year i n FormulaFuture
Value
Annual
Semiannually
Quarterly
Monthly
Daily (bankers’
rule)
Daily (exact
method)D. Continuous Compounding (Optional)
- Xiaoyi has deposited $2,199.50 in a 2-year CD paying 4.84% compounded continuously. How much will this account
be worth at the end of its term? - How much should I invest in order to have $5,000 at the end of 3 years if my account will earn 5.4% compounded
continuously? - Tessa deposited $1,056.25 in a 4-year CD paying 6.01% compounded daily. How much more interest would she earn if
the CD paid the same rate compounded continuously? - Suppose that you borrowed $850 at 11.3% compound interest for 5 years, but don’t remember how often the interest
compounds. What is the largest amount you could possibly need to pay off the loan at maturity?
E. Compound Interest With “Messy” Terms
- Find the future value of the given amount of money, assuming interest compounds at the stated interest rate and
compounding frequency for the given period of time.
a. $1,300 at 6.6% compounded monthly for 3½ years
b. $2,125 at 9.25% compounded quarterly for 5¾ years
c. $913.75 at 4% compounded daily (bankers’ rule) for 4½ years
d. $4,000 at 10.09% compounded monthly for 7 years and 5 months
e. $6,925.35 at 5½% compounded monthly for 63 months
f. $1,115.79 at 2^3 ⁄ 8 % compounded daily (bankers’ rule) for 4 years, 7 months, and 15 days.
g. $75,050.95 at 3.85% compounded daily (bankers’ rule) for 19 years, 2 months, and 28 days
h. $3,754.77 at 4.31% compounded daily (exact method) for 535 days- How much interest would you earn from a $4,200 deposit in 30 months if the interest rate is 5.64% compounded monthly?
112 Chapter 3 Compound Interest