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A sum of money amounts to 2420 in 2 years and 2662 in 3 years at compound interest. What is the rate of interest per annum?
8%
10%
12%
5%
10%
In compound interest, the amount at the end of one period acts as the principal for the next period. Since the duration is consecutive (year 2 to year 3), the interest earned in the third year is simply the interest on the amount at the end of the second year.
In compound interest, the amount at the end of one period acts as the principal for the next period. Since the duration is consecutive (year 2 to year 3), the interest earned in the third year is simply the interest on the amount at the end of the second year.
Think of compound interest like a snowball rolling down a hill; each year, the 'snowball' (the total amount) gets larger, so it picks up even more snow (interest) in the following year than it did previously.
A=P(1+100rтАЛ)n тАФ Compound interest formula for amount
I=An+1тАЛтИТAnтАЛ=AnтАЛ├Ч100rтАЛ тАФ Calculation of rate using consecutive years
The interest earned on the accumulated amount over one year is given by the difference between the amount at the end of year 3 and year 2. The rate r is then calculated using the simple interest formula applied to this one-year interval, where the principal is the amount at year 2. Mathematically, r=PrincipalInterestтАЛ├Ч100%.
Compound interest involves 'interest on interest'.
The difference between two consecutive year amounts represents the simple interest on the earlier amount for exactly one year.
For n=1 year, Compound Interest calculations simplify to Simple Interest logic.
Compounding yields exponential growth of capital over time.
Can lead to rapid debt accumulation for borrowers.
Banking and savings accounts.
Investment portfolio growth calculations.
Calculated interest: 2662тИТ2420=242.
Calculation: r=2420242тАЛ├Ч100=10%.
Option A is incorrect as 8% of 2420 is 193.6, which does not reach 2662.
B is correct тАФ The interest earned on the amount of 2420 for one year is 242, which equates to a 10% rate of interest.
When given consecutive years in compound interest problems, always calculate the interest as a percentage of the earlier year's amount to save time.
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