In: Finance
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
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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