Question

In: Finance

a) You took out a one-year loan for $3000 and agreed to pay it in three...

a) You took out a one-year loan for $3000 and agreed to pay it in three equal installments, one payment at the end of 1 months, a second payment at the end of 2 months, and a last payment at the end of the year. What is the size of each payment? Assume interest rate is 9%.

b) In part (a), suppose that you made three non-equal payments: the first was $600 at the end of 1 month, the second was $800 at the end of 2 months and the final payment was $X at the end of the year. What is the value of X if interest rate is 8%? Use the declining balance method.

please write down detail show all steps

Solutions

Expert Solution

a). - One year loan value today(or Present Value) = $3000

You agrred to pay in three equal installments, one payment at the end of 1 months, a second payment at the end of 2 months, and a last payment at the end of the year.

calculating the Value of equal Installments:-

where, r = periodic interest rate = 9%/12 = 0.75%

C = equal Installments

3000 = C*0.992556 + C*0.985167 + C*0.914238

3000 = C*[0.992556 + 0.985167 + 0.914238]

3000 = C*2.891961

C = $1037.36

So, the size of each payment is $1037.36

b). One year loan value today(or Present Value) = $3000

You will make three non-equal payments: the first was $600 at the end of 1 month, the second was $800 at the end of 2 months and the final payment was $X at the end of the year

Calculating the value of X:-

where, r = periodic interest rate = 8%/12 = 0.666666%

C1 = Payment in month 1 = $600

C2 = Payment in month 2 = $800

C12 = Payment in month 12

3000 = 596.0265 + 789.4391 +C12*0.923361

C12*0.923361 = 1614.5344

C12 = $1748.54

So, the value of X is $1748.54

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