5. A person invests a same amount of 80,000 in the two schemes for 3 years at the rate of interest of 4.5% per annum. If the scheme 1 is based on the simple interest and scheme 2 is based on the compound interest compounded annually, how much excess interest does the person earn in the scheme 2?
Answers
Answer:
To calculate the simple interest earned on an investment, you can use the formula:
I = P * r * t
Where:
I is the interest earned
P is the principal amount invested (in this case, 80,000)
r is the interest rate (in this case, 4.5%)
t is the length of the investment (in this case, 3 years)
So, the simple interest earned on the 80,000 investment at 4.5% per year for 3 years is:
I = 80,000 * 4.5% * 3 years = 10,800
The total amount the person will have at the end of the investment period, including the interest, will be 80,000 + 10,800 = 90,800.
To calculate the compound interest earned on an investment, you can use the formula:
A = P * (1 + r/n)^(n*t)
Where:
A is the total amount at the end of the investment period, including the interest
P is the principal amount invested (in this case, 80,000)
r is the interest rate (in this case, 4.5%)
t is the length of the investment (in this case, 3 years)
n is the number of times per year that the interest is compounded (in this case, annually, so n = 1)
So, the compound interest earned on the 80,000 investment at 4.5% per year for 3 years, compounded annually, is:
A = 80,000 * (1 + 4.5/1)^(1*3) = 84,794.25
The total amount the person will have at the end of the investment period, including the interest, will be 84,794.25.
To find out how much more interest the person earned in the compound interest scheme, you can subtract the amount of interest earned in the simple interest scheme from the amount of interest earned in the compound interest scheme:
84,794.25 - 90,800 = 4,005.75
So, the person earned an excess of 4,005.75 in the compound interest scheme.
Step-by-step explanation: