1. If you paid $550 to a loan company for the use of $8000 for 90 days, what annual rate of interest is the company charging? (Hint: Simple annual interest problem)
2. What is the purchase price of a 39-week "T-bill" (US Treasury note) with a maturity value of $4500 that earns an annual interest rate of 3.25 %? (Hint: Final amount A = $4500, length of loan (time) in years is 39 weeks / 52 weeks per year = 0.75 years)
3. How long (in years) will it take money to triple if it is invested at 7.0% compounded continuously? Round answer to nearest tenth of a year (Hint: Compound interest problem - problem states compounding is continuous, so we also know what formula to use).
4. What is the annual percentage yield (APY) for money invested at an annual rate of 4.45% compounded daily?
5. Advanced Insurance Company offers a "college education" annuity that pays 7.2% compounded quarterly. What equal quarterly deposit should be made into this annuity in order to have $200,000 for college expenses in 18 years? (Hint: This is a "sinking fund" problem with 7.2% interest compounded quarterly)
6. Mark makes his first deposit of $1500 into a Roth IRA earning 6.5% interest compounded annually at age 36. He continues to make an annual deposit of $1500 until he is 60 (25 deposits in all). With no additional deposits after age 60, the money in Mark's Roth IRA continues to earn 6.5% interest compounded annually until he retires at age 66. How much money is in Mark's Roth IRA when he retires?
(Hint: Part I is a "sinking fund" problem where we'll calculate FV only or the time Mark makes payments into his account. Part II takes the answer to Part I and sets it as P in a compound interest problem where we're solving for the amount in Mark's account when he retires: final amount A.)
7. The Smith's family takes out a 30-year mortgage at 4.25% compounded monthly after putting 20% down to buy a home valued at $220,000. Find:
a. the monthly payment
b. the unpaid balance after 10 years
c. the equity the family has built up in its house after 20 years of monthly payments, if the house's net market value 20 years from now is $300,000
(Hint: Mortgage loan scenarios are essentially amortization problems, and we use "present value of an annuity" formulas to solve them.
Part (a): Find PMT
Part (b): To find the unpaid balance after 10 years, we use the "present value" formulas again, only this time we're looking for PV when n = number of payments remaining to be made.
Part (c): "Equity" = (current market value of home) - (unpaid loan balance)