Combining Factors

8/11/2019 Combining Factors

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Module 11


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Single Sums of Money

Suppose you deposit $2,000 in an individualretirement account (IRA) that pays interest at 6%compounded monthly for the first two yearsand 9% compounded monthly for the next threeyears. Determine the balance at the end of fiveyears.


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Commercial Loans

One of the most important applications of

compound interest involves loans that arepaid off in installments over time. If the loanis to be repaid in equal periodic amounts(weekly, monthly, quarterly, or annually), it is

said to be an amortized loan.


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The annual percentage rate APR) is set bylenders, who are required to tell you what aloan will actually cost per year, expressed asan APR. Some lenders charge lower interest,

but add high fees; others do the reverse.Combining the fees with a year of interestcharges to give you the true annual interestrate, the APR allows you to compare thesetwo kinds of loans on equal terms.


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Fees are the expenses the lender will chargeto lend the money. The application fee coversprocessing expenses. Attorney fees pay thelenders attorney. Credit search fees cover

researching your credit history. Originationfees cover administrative costs andsometimes appraisal fees. All these fees addup very quickly and can substantially increasethe cost of your loan.


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Finance charges are the cost of borrowing.For most loans, they include all the interest,fees, service charges, points, credit-relatedinsurance premiums, and any other charges.


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The periodic interest rate is the interest thelender will charge on the amount you borrow.If lender also charges fees, the periodicinterest rate will not be the true interest rate.

The term of your loan is crucial indetermining its cost. Shorter terms meansqueezing larger amounts into fewerpayments. However, they also mean payinginterest for fewer years, saving a lot ofmoney.


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Suppose you intend to own or lease a vehiclefor 42 months. Consider the following threeways of financing the vehiclesay, a 2006BMW 325 Ci 2-D coupe:

Option A: Purchase the vehicle at the normalprice of $32,508, and pay for the vehicle over42 months with equal monthly payments at5.65% APR financing.

Option B: Purchase the vehicle at a discountprice of $31,020 to be paid immediately. Option C: Lease the vehicle for 42 months.


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The accompanying chart lists the items ofinterest under each option. For each option,

license, title, and registration fees, as well astaxes and insurance, are extra. For the leaseoption, the lessee must come up with $1,507.76at signing. This cash due at signing includes thefirst months lease payment of $513.76 and a

$994 administrative fee. The lease rate is basedon 60,000 miles over the life of the contract.There will be a surcharge at the rate of 18 centsper mile for any additional miles driven over60,000. No security deposit is required; however,a $395 disposition fee is due at the end of thelease, at which time the lessee has the option topurchase the car for $17,817. The lessee is alsoresponsible for excessive wear and use.


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If the funds that would be used to purchase thevehicle are presently earning 4.5% annual interestcompounded monthly, which financing option is abetter choice?


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Documents

Combining Factors