A $10000 loan is taken & is repaid by annual installments of $2000. Interest is charged on the outstanding debt at 10% p.a. find the number of years it takes for the mortgage to be repaid
Principal, P = $10,000
Annual Repayment, R = $2,000
Annual interest, a = 10% p.a.
Number of years to repay loan, n yrs
The formula for mortgage repayment is,
R = a.P / {1 - 1/(1+a)^n}
Rearranging,
{1 - 1/(1+a)^n} = a.P / R
1 - aP/R = 1/(1+a)^n
(1+a)^n = 1/(1 - aP/R)
(1+a)^n = R/(R - aP)
Substituting for the given values,
(1.1)^n = 2,000/(2,000 - 0.1*10,000)
(1.1)^n = 2,000/(1,000) = 2
n.ln(1.1) = ln(2)
n = ln(2)/ln(1.1) = {0.693147} / 0.09531
n = 7.27254 yrs
n = 7yrs 3 mths 8 days