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# Annuities Due, Number of Periods, Interest Rates, Future Values

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Calculating Annuities Due

You want to buy a new sports car from Muscle Motors for \$32,000. The contract is in the form of a 72-month annuity due at a 7.75 percent APR (compounded monthly). Your monthly payment will be \$? . (Round your answer to 2 decimal places, e.g. 32.16.)

Calculating the Number of Periods

At 12 percent interest, it would take years to double your money, and years to quadruple it. (Round your answer to 2 decimal places, e.g. 32.16.)

Calculating Interest Rates and Future Values

In 1895, the winner of a competition was paid \$180. In 2006, the winner's prize was \$2,568,000. This is a percent (Do not include the percent sign (%). Round your answer to 2 decimal places, e.g. 32.16.) increase in the winner's prize over this period. If the winner's prize increases at the same rate, it will be \$ in 2040. (Do not round your intermediate values. Round your answer to the nearest whole number, e.g. 32.)

#### Solution Summary

This solution involves calculations for annuities due, number of periods, interest rates, and future values.

\$2.19

## Concepts: BEP and TIE, Annuity vs. Annuity due, Loan Amortization, Present and Future Value

b. Briefly discuss the concept of relevant cash flows when evaluating a new project.

1- Explain the relationship between (i) discount rate and present value, and (ii) compound
rate and future value.

2- Why is the future value for an annuity due always higher than that of an ordinary
annuity?

3- Although the payment made on an amortized loan is constant, it can be decomposed
into two components. What are the TWO (2) components? Describe the patterns of each
component over time.

4- Your company has recently announced that its net income was lower than last year.
However, analysts found that the company's net cash flow increased. What factors could
explain this discrepancy?

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