If an amount of Rs 10,000/- is invested at a simple interest of 12% per annum, how much it will become at the end of 5 years ? And if this amount is invested at a compound interest of 10% per annum (the interest being compounded on yearly basis), how much it will become at the end of 5 years ? Also answer that the invested amount will be more at the end of 5 years in which case.
simple: 10000(1+.12*5)
compound: 10000(1+.10)^5
evaluate and compare.
To calculate the simple interest, we can use the formula:
Simple Interest = (Principal * Rate * Time) / 100
Given:
Principal (P) = Rs 10,000/-
Rate (R) = 12% per annum
Time (T) = 5 years
Substituting these values into the formula, we get:
Simple Interest = (10,000 * 12 * 5) / 100
= 6,000
So, at the end of 5 years, the amount will become:
Amount = Principal + Simple Interest
= 10,000 + 6,000
= Rs 16,000/-
Now, let's calculate the compound interest using the formula:
Compound Interest = Principal * ((1 + Rate/100)^Time - 1)
Principal (P) and Time (T) remain the same as before.
Given:
Rate (R) = 10% per annum
Substituting these values into the formula, we get:
Compound Interest = 10,000 * ((1 + 10/100)^5 - 1)
= 10,000 * ((1 + 0.1)^5 - 1)
= 10,000 * (1.1^5 - 1)
= 10,000 * (1.61051 - 1)
= 6,105.10
So, at the end of 5 years, the amount will become:
Amount = Principal + Compound Interest
= 10,000 + 6,105.10
= Rs 16,105.10
Comparing both amounts, we can see that the amount at the end of 5 years is higher when investing at compound interest (Rs 16,105.10) compared to simple interest (Rs 16,000). Hence, the invested amount is more at the end of 5 years when using compound interest.