NUMBER SENSE, ESTIMATION, AND FINANCIAL COMPUTATIONS 5

NumberSense, Estimation, and Financial Computations

Letthe total value of the appliances, P = $8,000

Letthe annual interest rate, r = 25% this can be depicted as 0.25 indecimal form

Sincethe bill is not paid within the agreed period, the interest rate fortwo years will apply

Simpleinterest = P * r * t

=8,000 * 0.25 * 2

Simpleinterest for the two years = $4,000

So,an interest of $4,000 will be paid in case the bill is paid 1 daylate

Totalbill that will be paid = P + interest

=$8,000 + $4,000

Totalbill = $12,000

Incase the store charges compound interest which is compounded daily,then the following formula will be used A = P (1 + r/n)^{nt}

Letthe days in the year = 366 this implies that n = 1/366 = 0.002732

Totalbill payable in case interest is compounded daily = 8,000 (1 +0.25/0.002732)^{0.002732*2}

=8,000 (1 + 91.508053)^{0.005464}

=8,000 (92.508053)^{0.005464}

(92.508053)^{0.005464}= 1.025046

Totalbill = 8,000 (1.025046)

=8,200.368

Thisis approximately $8,201

Theamount for two years would be $8201 however, since the amount iscompounded daily and the amount is paid one day late, then theinterest accumulated for the one extra day will be charged by thestore. So, $8201 gives the principal amount to be used for the oneday interest.

Therefore,the amount interest for being one day late will be I = 8,201 * 0.25* 0.002732

=5.601283

=$6

Thus,the amount payable two years plus one day would be 8,201 + 6

=$8,207

Therefore,the interest charged on the appliances by the store in case it iscompounded daily at a rate of 0.25 would be $8,207 – $8,000

=$ 207

Fromthe results of the calculations, there are several differences amidsimple and compound interest. One of the differences amid the two isthat simple interest is calculated directly by multiplying the amountpayable at the time of buying by the time period when the amount willbe settled and the rate that is charged on the amount payableannually. However, in the case of compound interest, the formula A =P (1 + r/n)^{nt}has to be used less the initial amount. This implies that unlike thecalculations in simple interest where P * r * t is used directly,compound interest is indirect. Another difference between the simpleand compound interest is that, in simple interest, only the principalamount earns interest. However, in compound interest both theprincipal amount and the interest of the previous period earninterest. This is because the principal amount for the next period isdetermined by the principal amount of the previous period plus theamount of interest earned during the period. Another differencebetween the two is that compound interest is calculated periodicallyand the total interest is found by adding all the interest amountsfor the different periods. When it comes to computing simpleinterest, this is calculated as one and there is no adding up ofinterests for different periods. Also, when calculating the simpleinterest, the principal amount remains constant throughout the periodunder consideration however, this is not the case when it comes tocompound interest because the principal amount keeps on changing fromone period to the other. In addition, the interest amount yielded bythe two methods is usually different and is usually determined by thecompounding period.

Deferredbilling describes an arrangement where shoppers and sellers can reachan agreement for the sale of an item, whereby the seller allows thebuyer to make payment at a future date for the item being purchased.The future payment usually attracts interest that the buyer and theseller have to agree upon. Sometimes, the deferred billing option isbeneficial to the shoppers, but at times it may not be of help. Themajor benefit that comes with using deferred billing option toshoppers is that shoppers can be in a position to acquire therequired item even though they do not have the full amount requiredfor purchasing an item. At times, due to inflation, an item bought byshoppers at a certain amount may be charged higher than what theshoppers could have paid using the deferred billing. In such ascenario, shoppers are likely to benefit a lot because they arecapable of obtaining what they need without enough money and at acheaper rate.

Nevertheless,the deferred billing option may not be helpful to shoppers at timesbecause the shoppers may end being charged high amounts of intereststhat even goes beyond the actual amount that the shoppers could havepaid even when inflation and other factors are considered. This isusually the case, when the rates of interest are set to be very highby the sellers. In such a scenario, the shoppers using deferredbilling option would end up being charged a very high price for anitem purchased.