What sum (in Rs) given on loan for two years with scheme of retum on the basis of compound interest at a
yearly rate of 10% will correspond to repayment through equal monthly installments of Rs 9075?
Answers
Given :- What sum (in Rs) given on loan for two years with scheme of retum on the basis of compound interest at a
yearly rate of 10% will correspond to repayment through equal monthly installments of Rs 9075 ?
Solution :-
Let us assume that, required sum is Rs.P .
Than, from given data we have :-
- Principal = Rs.P
- Rate = R = 10% compounded annually = (10/12)% monthly .
- Time = T = 2 years = 2 * 12 = 24 months.
- Monthly installment = Rs.9075 .
we know that,
- Monthly installment = [P * (R/100)] * {1 + (R/100)}^(T)[{1+(R/ 100)}^(T)- 1]
Putting all values we get,
→ 9075 = [P * (10/1200)] * {1+ (10/1200)}²⁴ * [{(1+ (10/1200)}²⁴ - 1]
→ 9075 = (P/120) * (121/120)²⁴ * {(121/120)²⁴ - 1}
→ P = Rs.196670 (Ans.)
Hence, Rs.196670 was given to loan for 2 years.
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Given : loan for two years with scheme of retum on the basis of compound interest at a yearly rate of 10% will correspond to repayment through equal monthly installments of Rs 9075
To Find : Amount of Loan
Solution:
EMI Formula = [P x (R/100) x (1+(R/100)ⁿ]/[(1+(R/100)ⁿ-1]
EMI = 9075
R = 10 % per annum = 10/12 % per month
P = ?
n =24 (2 years = 24 Months )
9075 = (P * 10/1200 ) * ( 1 + 10/1200)²⁴ / (( 1 + 10/1200)²⁴ - 1)
=> P = 196670 Rs
Loan Amount = 196670 Rs
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