Mohammed borrowed $2500 at 4% p.a. compound interest. He repays $600 at the end of each year. During which year will the debt finish?
Shiv Answered question May 9, 2023
The loan Equation is given as follows,
L = E(1-(1+i)^-n)/i
Where
L = loan amount = 2500
E = Annual repayment = 600
i = Annual interest rate = 4%
n = Time in years
There,
2500 = 600*(1-(1+4%)^-n)/.04
2500*.04/600 = (1-(1+4%)^-n)
0.16666 = 1-(1.04)^-n
1.04^n = 0.8333
taking log of both sides
log1.04^-n = log0.8333
-n* log1.04 = 10g0.8333
-n* 0.017033 = -0.079146
n = 0.079146/0.017033 = 4.64 years
debt will finish in 4.64 years
Shiv Answered question May 9, 2023
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