To find the interest rate when an investment is compounded annually, you can use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A = the final amount
P = the principal amount (initial investment)
r = the annual interest rate (in decimal form)
n = the number of times interest is compounded per year
t = the number of years
In this case:
P = €696
A = €881.85
t = 5 years
n = 1 (compounded annually)
We need to find 'r' (the annual interest rate).
881.85 = 696(1 + r/1)^(1*5)
Now, let's isolate 'r':
1 + r = (881.85 / 696)^(1/5)
1 + r ≈ 1.26704 (rounded to five decimal places)
Now, subtract 1 from both sides to find 'r':
r ≈ 1.26704 - 1 ≈ 0.26704
So, the annual interest rate is approximately 0.26704, which is equivalent to 26.704% when expressed as a percentage. Therefore, the interest rate was approximately 26.704% per year when compounded annually.
Answers & Comments
Verified answer
Answer:
To find the interest rate when an investment is compounded annually, you can use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A = the final amount
P = the principal amount (initial investment)
r = the annual interest rate (in decimal form)
n = the number of times interest is compounded per year
t = the number of years
In this case:
P = €696
A = €881.85
t = 5 years
n = 1 (compounded annually)
We need to find 'r' (the annual interest rate).
881.85 = 696(1 + r/1)^(1*5)
Now, let's isolate 'r':
1 + r = (881.85 / 696)^(1/5)
1 + r ≈ 1.26704 (rounded to five decimal places)
Now, subtract 1 from both sides to find 'r':
r ≈ 1.26704 - 1 ≈ 0.26704
So, the annual interest rate is approximately 0.26704, which is equivalent to 26.704% when expressed as a percentage. Therefore, the interest rate was approximately 26.704% per year when compounded annually.
Answer:
the interest rate is 26.704 % per annum