scenario: Your children\'s museum isgowing and schools from al over southern Mda

Question

scenario: Your children's museum isgowing and schools from al over southern Mdaho want to visit and brinEstudents applying for grant money the purchase of a 2015 30-passenger bus. You wilbe buring it from The Bus The price will be $82.000. There are two finu nting options and you need to Est both in the gant. Al Fived installment loan from the m 12 years at 6.5% BI Fixed instalment loan trom a government agency lender: 7 years at 2.75% Determine the following The monthly payments and total interest for loan A 20 The monthly payments and total interest for loan B, Compare the monthly payments and totalinteresttor the two loans. State your recommendation, as you will ist in the park application using data from your caloulations

Explanation / Answer

The formula for computing the equated monthly installment is EMI = P[ r(1+r)n]/[ (1+r)n -1] where P is the amount of loan, r is the monthly rate of interest in decimals and n is the number ofmonthly installments.

A). For the 1st loan, P = $ 82,000, r = (6.5/100)*1/12 = 6.5/1200 and n = 12*12 = 144

Then the EMI = 82000[(6.5/1200)*(1+6.5/1200)144]/[(1+6.5/1200)144-1] = 444.167(1206.5/1200)144/[(1206.5/1200)144-1] = 444.167(2.17688531/1.17688531) = 444.167*1.849700469 = $ 821.58( on rounding off to the nearest cent). The total amount repaid is $ 821.58 *144 = $118307.52 so that the amount of interest is 118307.52-82000 = $ 36307.52

B) For the 2nd loan, P = $ 82,000, r = (2.75/100)*1/12 = 2.75/1200 and n = 7*12 = 84

Then the EMI = 82000[2.75/1200*(1+2.75/1200)84]/[(1+2.75/1200)84-1] = 187.9167(1202.75/1200)84/[(1202.75/1200)84-1] = 187.9167(1.212009546/0. 212009546) = 187.9167*5.716768744= $1074.28 ( on rounding off to the nearest cent). The total amount repaid is $ 1074.28 *84 = $90239.52 so that the amount of interest is90239.52-82000 = $ 8239.52

C) the EMI for the 1st and the 2nd loans are $ 821.58 and $1074.28 respectively and the interest paid obn the loan are $ 36307.52 and $ 8239.52 respectively.

D) If the museum can afford a higher installment , then the 2nd loan would be more cost-effective.

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