A person amortizes a loan of Rs 1500000 for renovation of his house by 8 years mortgage at the rate of 12% p.a. compounded monthly. Find the total interest paid.
(Given $(1.01)^{96}=2.5993, (1.01)^{57}=1.7633)$
Answer & explanation
Correct answer: option 1
The correct answer is option (1) : ₹84039.60
Given $P=₹1500000, n=12×8=96\, months $
i.e $i=\frac{12}{1200}=0.01$
$EMI=\frac{1500000×0.01(1.01)^{96}}{(1.01)^{96}-1}$
$=₹24379.10$
Principal outstanding at beginning of 40th month
$⇒\frac{EMI[(1+i)^{n-K+1}-1}{i(1+i)^{n-k+1}}$
$⇒\frac{24379.10[(1.01)^{57}-1]}{0.01(1.01)^{57}}$
$⇒₹1055326.2$
Interest paid in 40th payment
$=EMI[(1+i)^{90-40+1}-1]$
$=(1+i)^{96-40+1}$
$=\frac{24379.10×0.7633}{1.7633}$
$=₹10553.26$
Principal contained in 40th payment $= EMI-$ Interest paid in 40th payment
$= ₹24379.10-₹10553.26$
$=₹12825.84$
Total interest paid $= n×EMI-P$
$=96×24379.10-1500000$
$=₹84039.60$