It looks like your query is incomplete - specifically, the principal amount (Rs 0 is likely a placeholder) and the interest rate per annum are missing. To calculate the equal yearly installments for a loan with compound interest, I need these details:
- Principal amount borrowed (P)
- Annual compound interest rate (r%)
- Number of years (n = 2)
- Number of installments (2 equal yearly installments)
How to Calculate Equal Yearly Installments with Compound Interest
Assuming:
- Principal = P
- Annual interest rate = r% (expressed as a decimal, e.g., 10% = 0.10)
- Number of years = 2
- Number of equal installments = 2 (one at the end of each year)
Step 1: Understand the problem
Raghav borrows P rupees, to be repaid in 2 equal installments at the end of each year, with compound interest applied annually.
Step 2: Formula for equal installments (EMI)
The installments are like an annuity that pays off the loan with compound interest. The formula for each installment (A) is:
A=P×r(1+r)n(1+r)n−1A=P\times \frac{r(1+r)^n}{(1+r)^n-1}A=P×(1+r)n−1r(1+r)n
Where:
- PPP = Principal
- rrr = annual interest rate in decimal
- nnn = number of installments (2)
Example Calculation
Suppose:
- Principal P=10,000P=10,000P=10,000 Rs
- Interest rate r=10%=0.10r=10%=0.10r=10%=0.10
- Number of installments n=2n=2n=2
Calculate:
A=10,000×0.10×(1+0.10)2(1+0.10)2−1=10,000×0.10×1.211.21−1=10,000×0.1210.21≈10,000×0.5762=5762A=10,000\times \frac{0.10\times (1+0.10)^2}{(1+0.10)^2-1}=10,000\times \frac{0.10\times 1.21}{1.21-1}=10,000\times \frac{0.121}{0.21}\approx 10,000\times 0.5762=5762A=10,000×(1+0.10)2−10.10×(1+0.10)2=10,000×1.21−10.10×1.21=10,000×0.210.121≈10,000×0.5762=5762
So, each installment will be approximately Rs 5,762.
Please provide the principal amount and interest rate so I can compute the
exact installments for you!
