Question

Fatima borrows rupees 12580 12% per annum for 3 years at simple interest and Radha borrows the same sum for the same time at 10% per annum compounded annually why was more interest and pay how much

Answer 1

Answer:

Fatima's interest is 4528.80

Radha's interest is 4163.98

Although Fatima's interest was simple interest, the higher rate and quite short time period have meant that she has accrued more interest than Radha.  However, if the loan were just a bit longer, because of the effects of compounding, Radha would end up with more interest than Fatima, even though the interest rate is lower.

Step-by-step explanation:

There is no mention of payments on these loans, so we will have to suppose that no payments are made in those 3 years.

Since Fatima's loan uses simple interest, the interest each year is just 12% of the principal.  So each year, the interest accrued is

12% of 12580 = 0.12 × 12580 = 1509.60.

Over 3 years then, the total interest is 3 × 1509.6 = 4528.80.

In the case of Radha, the interest is compounding, so each year the interest is calculated and added to the total owing, so that the next year the interest is calculated on that new total.  So:

At the end of year 1, interest is 10% of 12580 = 0.1 × 12580 = 1258.  The new total owing is 12580 + 1258 = 13838.

At the end of year 2, interest is 10% of 13838 = 1383.80.  The new total owing is 13838 + 1383.80 = 15221.80.

At the end of year 3, interest is 10% of 15221.80 = 1522.18.  The new total owing is 15221.80 + 1522.18 = 16743.98.

So the total amount of interest accrued by Radha is

16743.98 - 12580 = 4163.98.