A 4% loan of $20,000 is to be repaid by level annual installments. The principal in the 4th installment is $450. Find the amount of each installment.

Explanation:

Please note that this question we have to do by hit and trail method. Every annual payment has 2 components,

Interest and Principal repayment

Interest is higher at the beginning and principal repayment is lower. We have not been given the time for the loan.

So i will tell you how to calculate the Total annual installment by hand

and then we will make table of payments to see if we are getting 450 principal repayment in month 4

We will do 3-4 iterations to get the answer

Loan Amount = 20,000

Rate = 4%

Principal repayment in year 4 = 450

Let say time = n years

Annual installment = Loan amount * ( rate * ( 1+rate ) ^n ) / ( ( 1 + rate ) ^n -1 )

assume n = 25 years

Annual installment = 20,000 * ( 0.04* ( 1.04 ) ^ 25 ) / ( ( 1.04 ) ^25 -1 ) = 1280.24

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