d) ABC has taken a loan of $700000 from ICICI at the rate of 8% compounded quarterly. The amount has to be repaid in 6 annual instalments. Make a loan repayment schedule.
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The loan repayment process is by installments which are otherwise called an annuity. For us to get the capital repaid in installments we use an annuity function for obtaining the present value of the loan.
We first convert the interest into an annual rate:
1+i=(1+0.08/3)^3
We get 8.22% as the annual rate.
We then get the present value of the loan as follows:
Let X be the present value, then:
X×[(1-(1.0822)^-6)÷0.0822]=4.5922X
4.5922X=700000
thus X=152432.39
X is the capital to be repaid every year. The loan schedule is:
YEAR1:interest=0.0822×700000=57540,capital repaid=152432.39-57540=94892.39,capital outstanding=700000-94892.39=605107.61
YEAR2:interest=0.0822×605107.61=49739.85,capital repaid=152432.39-49739.85=102692.54,capital outstanding =605107.61-102692.54=502415.07
YEAR3:interest=0.0822×502415.07=41298.52,capital repaid=152432.39-41298.52=111133.87,capital outstanding =502415.07-111133.87=391281.20
YEAR4:interest=0.0822×391281.20=32163.31,capital repaid =152432. 39-32163.31=120269.08,capital outstanding=391281.20-120269.08=271012.12
YEAR5:interest=0.0822×271012.12=22277.20,capital repaid =152432.39-22277.20=130155.19,capital outstanding=271012.12-130155.19=140856.93
YEAR6:interest=0.0822×140856.93=11578.44,capital repaid=152432.39-11578.44=140853.95,capital outstanding =140856.93-140853.95=2.98
This is the loan repayment schedule.
The image below gives more details.
We first convert the interest into an annual rate:
1+i=(1+0.08/3)^3
We get 8.22% as the annual rate.
We then get the present value of the loan as follows:
Let X be the present value, then:
X×[(1-(1.0822)^-6)÷0.0822]=4.5922X
4.5922X=700000
thus X=152432.39
X is the capital to be repaid every year. The loan schedule is:
YEAR1:interest=0.0822×700000=57540,capital repaid=152432.39-57540=94892.39,capital outstanding=700000-94892.39=605107.61
YEAR2:interest=0.0822×605107.61=49739.85,capital repaid=152432.39-49739.85=102692.54,capital outstanding =605107.61-102692.54=502415.07
YEAR3:interest=0.0822×502415.07=41298.52,capital repaid=152432.39-41298.52=111133.87,capital outstanding =502415.07-111133.87=391281.20
YEAR4:interest=0.0822×391281.20=32163.31,capital repaid =152432. 39-32163.31=120269.08,capital outstanding=391281.20-120269.08=271012.12
YEAR5:interest=0.0822×271012.12=22277.20,capital repaid =152432.39-22277.20=130155.19,capital outstanding=271012.12-130155.19=140856.93
YEAR6:interest=0.0822×140856.93=11578.44,capital repaid=152432.39-11578.44=140853.95,capital outstanding =140856.93-140853.95=2.98
This is the loan repayment schedule.
The image below gives more details.
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