# Compound Annually Grow Interest Accountability

User Generated

avhavn83

Mathematics

## Description

1. How long did it take \$4,625 earning 7.875% compounded annually to grow to \$8,481.61?

2. The current balance on a loan is \$3,837.30. If the interest rate on the loan is 10% compounded monthly, how long ago was the \$2,870 loan made?

3. What is the remaining time until the maturity date of a \$10,000 strip bond if it is purchased for \$4,011.33 to yield 6.4% compounded semiannually until maturity?

4. A few years ago, Avtar invested \$6,000 in a compound-interest GIC that earned 4.5% compounded semiannually. He recently received the maturity value of \$7,168.99. What was the term of the GIC?

5. Rounded to the nearest month, how long will it take an investment to double if it earns: a. 8.4% cm? b. 10.5% csa?

6. Rounded to the nearest month, how long will it take an investment to quadruple if it earns: a. 8% ca? b. 9% csa?

7. Which interest rate would you prefer to earn on a three-year GIC: 6% compounded monthly, 6.1% compounded quarterly, 6.2% compounded semiannually or 6.3% compounded annually?

8. What is the effective rate of interest on a credit card that calculates interest at a rate of 1.8% per month?

9. If the nominal rate of interest paid on a savings account is 2% compounded monthly, what is the effective rate of interest?

10. If a \$5,000 investment grew to \$6450 in 30 months of monthly compounding, what effective rate of return was the investment earning?

11. Lisa is offered a loan from a bank at 7.2% compounded monthly. A credit union offers similar term, but at a rate of 7.4% compounded semiannually. Which loan should she accept? Present calculations that support your answer.

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## Explanation & Answer

See attached

1. How long did it take \$4,625 earning 7.875% compounded annually to grow to \$8,481.61?
FV= PV(1+r)n
n= ln(FV/PV)/ ln(1+r)
n=ln(8481.61/4625)/ln(1+7.875%)
n=8 years
2. The current balance on a loan is \$3,837.30. If the interest rate on the loan is 10% compounded
monthly, how long ago was the \$2,870 loan made?
FV= PV(1+r)n
n= ln(FV/PV)/ ln(1+r)
n=ln(8481.61/4625)/ln(1+10%/12)
n= 35 months

3. What is the remaining time until the maturity date of a \$10,000 strip bond if it is purchased for
\$4,011.33 to yield 6.4% compounded semiannually until maturity?
FV= PV(1+r)n
n= ln(FV/PV)/ ln(1+r)
n=ln(10000/4011.33)/ln(1+6.4%/2)
n= 29 ...

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