a loan is amorized over five years with monthly payments at a nominal interest rate of 9% compounded monthly.the first payment is 1000 and is to be paid one month from the date of the loan.each succeeding monthly payment will be 2% lower than the prior payment.Calculate te outstanding loan balance immediately after the 40th payment is made.
We have provided with the information that ,
interest rate of 9% compounded monthly.
So i = 9 % /12 months
so i = 0.75
the first payment is 1000 and is to be paid one month
Each succeeding monthly payment will be 2% lower than the prior payment
So first payment is 1000
second payment is (1000- 2%(1000))
Like as follow
1000, 100(0.98), 1000(0.98)2 …………10000(0.98)58
the outstanding loan balance immediately after the 40th payment is made is Calculate as follow
That is Kt = 1000(0.98)t−1 then
OB40 = K41v+K42v 2 + K43v 3 + · · · + K60v 20
== 1000(0.98)40v + 1000(0.98)41v 2 + 1000(0.98)42v 3………… + · · · + 1000(0.98)59v 20
== 1000(0.98)40v ( 1 + (0.98v) + (0.98v) 2 + · · · + (0.98v) 19)
= = 1000(0.98)40v * 1 − (0.98v)20/ 1 − (0.98v)
== 6889.114798
Answer: 6889
