Question

Construct an amortization schedule for a six-year, RM20,000 loan at 7% interest compounded annually

a) If the first payment is made one year from now.

Ans: P = RM 4,195.92

b) If the first payment is made immediately.

Ans: P = RM 3,921.42

Answer 1

(a) If the first payment is made from next year

Loan Amount = P = 20000

Let the amount paid annually be x

Interest Rate = r = 7% or 0.07

Tenure = n = 6 years

Hence, the sum of present value of annual payments must be equal to the value of the loan amount

=> X/(1+r) + X/(1+r)² +....+ X/(1+r)^N = P

=> X[1- (1+r)^-N]/r = P

=> X = rP(1+r)^N/[(1+r)^N-1]

=> X = 20000*( 0.07)*(1+ 0.07)⁶/((1+ 0.07)⁶-1) = $4195.92

(b) if the first payment is made now

Loan Amount = P = 20000

Let the amount paid annually be x

Interest Rate = r = 7% or 0.07

Tenure = n = 6 years

Hence, the sum of present value of annual payments must be equal to the value of the loan amount

=> X + X/(1+r) + X/(1+r)² +....+ X/(1+r)^N-1 = P

=> X + X[1- (1+r)^-(N-1)]/r = P

=> X = rP(1+r)^N-1/[r(1+r)^N-1 + (1+r)^N-1-1] = rP(1+r)^N-1/[(1+r)^N-1]

=> X = = 20000*( 0.07)*(1+ 0.07)⁵/ [(1+0.07)⁶-1] = $3921.42