An annual instalment of ₹2,200 will discharge a debt of ₹ y due in 3 years at 14.5% simple interest per annum. What is the value of y? (Note: instalments will be paid at the end of year 1, year 2 and year 3.)

Correct option is B

Given:
Annual instalment = ₹2200
Time = 3 years
Rate = 14.5% p.a. (Simple Interest)

Formula Used:

​$$\text{Future Value} = A \times (1 + r \cdot t)$$​

Where:

A = Instalment

r = rate of interest

t = Number of years interest is earned

Solution: ​

rate of interest, r = $$\frac{14.5}{100} = 0.145$$​

1st instalment (paid at end of year 1, earns 2 years interest):

​$$2200 \times (1 + 0.145 \times 2) = 2200 \times 1.29 = 2838$$​

2nd instalment (paid at end of year 2, earns 1 year interest):

​$$2200 \times (1 + 0.145 \times 1) = 2200 \times 1.145 = 2519$$​

3rd instalment (paid at end of year 3, no interest):

= 2200

Total debt (y) = 2838 + 2519 + 2200 = ₹7557

∴ The value of y is ₹7557.

Thus, the correct option is (b) 7557