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1 May 2019

The number of compounding periods can greatly affect the amount of interest (as a percent or in real value) paid when considering loans. The compounding frequency can also affect investments through which we earn interest. How is this? Also, how do we adjust the TVM formula to account for compounding periods?

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Hubert Koch
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2 May 2019

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Problem 1: $3,000 is invested at 7.2% interest. Find the total amount (A) at the end of 5 years if:
a.) Simple interest is earned. (see the "Simple Interest Example" tab)
b.) Interest is compounded annually (see the "Compound Interest Illustration" tab)
c.) Interest is compounded quarterly (see the "Other Compounding Periods" tab)
d.) Interest is compounded monthly (see the "Other Compounding Periods" tab)
Problem 2: A department store charges 12% interest on the unpaid balance of customer charge accounts.
A customer owes $135, and the bill goes unpaid for 4 months. How much will the customer have to
repay after 4 months? Interest is compounded monthly (note that the 12% is an annual rate). (see the "Other Compounding Periods" tab)
Problem 3: A typical family of four spends approximately $600 per month for food. Food costs are
predicted to rise by 4.8% per year for the next 5 years. In five years, how much should
the family budget per month for food? Treat this as compound annual growth. (see the "Compound Interest Illustration" tab)
(assume annual compounding)
Problem 4a: A couple plans to begin saving money for a down payment toward the purchase of a home.
They plan to purchase a home 4 years from now. Right now, home prices are predicted
to rise by 5% per year for the next 5 years. If this prediction is accurate, how much
can this couple expect to pay in 4 years for a home that is currently valued at $210,000?
(what will be the total sales price in 4 years of a home worth $210,000 today?) (see the "Compound Interest Illustration" tab)
Problem 4b: The couple wants to have a 20% down payment on the purchase price in 4 years. Suppose they
have found a mutual fund that earns an average of 8% per year. How much should they invest in the
mutual fund today in order to have enough for a down payment in 4 years?
Assume annual compounding.
(Find the down payment first - that will be their "A" or future value of what they will invest)
(see the "Other Problem Types" tab - we are trying to find the principal or present value to be invested to grow to the down payment amount)
Problem 5: An electric company predicts that the cost of electricity will rise at the rate of 2% per
year for the next ten years. If the average monthly electricity for consumers in this area
is $225, predict the monthly amount that consumers can expect to pay 10 years from now.
(see the "Compound Interest Illustration" tab)

(1)

It took her 9 more months but Marina has managed to save thefull $725 plus more to cover fees to pay off the pay-day loancompany. However, she forgot to account for the interest that hadbeen compounding over time. Consider it is now 275 days later, theremaining loan was $725 and the APR is 47% compoundeddaily.

What is the total amount that Marina must now pay in order topay off her the loan, accounting for interest?

What is the total amount of interest paid (not includingfees)?

(2)

Tony is saving up to go traveling after graduation. How muchwill he have if he can put $100 at the beginning of every month,for the full four years he is in school, into his high-interestsavings account which earns 1.95% interest?

How much interest will be earned?

(3)

Anna also wants to travel after graduation but she isn’t workingwhile in school so she won’t be able to put money aside regularly.However, her grandmother gave her the generous gift of $2500 forher birthday and suggested she invest it in a GIC because it’s lowrisk. She shopped around and found a 4 year GIC investment thatearns 2.8% interest annually.

How much will Anna have at the end of her four yearinvestment?

How much interest will be earned?

How much interest will be earned due to compounding*?

*calculate simple interest using the simple interest formula,then compare to the total interest earned to discover the impact ofcompounding the interest

I. Fill in the blank using a number of terms listed below (@1 point). Annuity due, Asset Mgmt ratio, Call, Comparisons, Comparative ratio analysis, Corporation, Covered, Current Ratio, DSO, Du Pont Equation , Equal, Future performance, Greater, Higher, In-the-money, Less, Liquidity, Lower, Option, Ordinary Annuity, Out-of-the-money, Percentage, Perpetuity, Put, PV, Quick, Reduced, TIE, TATO, Trend Analysis, Writer 11. The payment or receipt of equal amounts, at the end of a series of equal periods, for a specified amount of time is called a(n) _______________. 12. When a loan is amortized over a five year term, the amount of interest paid is ________________ each year. 13. You have just won a $5 million lottery to be received in twenty annual equal payments of $250,000. What will happen to the present value of your winnings if the interest rate increases? It will be worth _________________. 14. The more frequent the compounding the _________________ the effective interest rate. 15. More frequent compounding results in _______________ future values and _______________ present values than less frequent compounding at the same nominal interest rate. 16. A(n) _______________ is a financial instrument that agrees to pay an equal amount of money per period into the indefinite future (i.e. forever). 17. A(n) _________________ is a contract which gives its holder the right to buy(or sell) an asset at some predetermined price within a specified period of time. 18. The seller of an option is called the option __________________. 19. An investor who writes call options against stock held in his or her portfolio is said to be selling _______________ options. 20. When the exercise price exceeds the current stock price, a call option is said to be _____________________; however, when the exercise price is less than the current price of the underlying stock, a call option is _________________. 21. An option which gives you the right to sell a stock at a specified price within some future period is called a(n) ______________ option.

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