12. A certain sum of money amounts to 7 300 in 2 years and 315 in 3 years
The rate of interest compounded annually is
Answers
Step-by-step explanation:
300 = P(1+r/100)²
315 = P(1+r/100)³
315/300 = (1+r/100)
315/300 = (100+r)/100
105 = 100+r
r = 5
Answer:
The correct answer is : 5%
Step-by-step explanation:
Let's call the principal amount of money "P" and the annual interest rate "r". We know that the interest is compounded annually, which means that at the end of each year, the interest earned is added to the principal, and then the new total amount earns interest for the following year.
After 2 years, the amount is 7,300. This means that:
P(1 + r)^2 = 7,300
After 3 years, the amount is 7,615 (315 + 7,300). This means that:
P(1 + r)^3 = 7,615
We can solve for P by dividing the second equation by the first equation:
(1 + r)^3 / (1 + r)^2 = 7,615 / 7,300
1 + r = 1.05
r = 0.05
So the annual interest rate is 5%.
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