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# Interest, Annuity, Installment loan, Mortgage

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1. Define simple interest and compound interest. Explain the difference between each.

2. Define annual percentage rate (APR). What effect does frequency of compounding have on the annual percentage yield (APY)? What condition would exist if the APR = APY?

3. What is an ordinary annuity? What is an annuity due? Which is more prevalent in apartment leases?

4. A very smart child understands annuities and wishes to invest part of his allowance each week to save up for college. The child's parents figure, they would kick in with matching funds, so each month, he deposits a total of \$50. Let us suppose that the child continues from age 5 to age 20. Given a fixed APR of 5%, what might the child expect to have at age 20?

5. What is an example of an installment loan? What type of installment loan does not require the borrower to pay off the balance?

6. Explain the difference between a fixed rate and adjustable rate mortgage.

## SOLUTION This solution is FREE courtesy of BrainMass!

1. Interest. Define simple interest and compound interest. Explain the difference between each.
Simple interest is a specific amount paid on the principle of an investment. Compound interest adds this amount to the principle and interest is paid on this combined amount. In general, simple interest pays a fixed rate and compound interest pays an increasing rate.
2. APR. Define annual percentage rate. What effect does frequency of compounding have on the annual percentage yield (APY)? What condition would exist if the APR = APY?
Annual percentage rate is the amount you will pay on a loan over the course of a year. The more frequently the interest is compound, the more the APY will increase. This is the same principal as compound interest, except in terms of interest paid. If APR = APY, then the interest is only compounded once a year and is effectively simple interest.
3. Annuities. What is an ordinary annuity? What is an annuity due? Which is more prevalent in apartment leases?
An ordinary annuity is a fixed payment placed at the end of a fixed point of time. An annuity due is a fixed payment placed at the beginning of a fixed point of time. Apartment leases are more commonly annuity dues because rent is expected to be paid at the beginning of each month.
4. A very smart child understands annuities and wishes to invest part of his allowance each week to save up for college. The childÃ¢â‚¬â„¢s parents figure, they would kick in with matching funds, so each month, he deposits a total of \$50. LetÃ¢â‚¬â„¢s suppose that the child continues from age 5 to age 20. Given a fixed APR of 5%, what might the child expect to have at age 20?
You can use this formula to solve:

i is the interest rate, M is the deposit amount (\$1,200 because the child is paying \$50 and the parents are paying \$50 over the course of 12 months), n is the number of times interest is paid (in this case 15 years), and q is the number of times interest is paid in a year (once).

5. Installment loan. What is an example of an installment loan? What type of installment loan does not require the borrower to pay off the balance?
An example of an installment loan is a mortgage or a student loan. In these loans, a payment is made at fixed intervals. A credit card is an example of an open-ended installment loan where the borrower does not need to pay off the balance but needs to pay the interest and finance charges.
6. Mortgages. Explain the difference between a fixed rate and adjustable rate mortgage
A fixed rate mortgage charges a fixed rate over the course of the loan. An adjustable rate mortgage has a variable interest rate the can change during the life of the loan.

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