A bank pays 10% compounded annually on its three-year fixed deposit account. At the end of the three years, a 3% bonus on the final amount will be paid. find the effective interest rate that will be earned on this scheme
1.1^3 * 1.03 = 1.37093
∛1.37093 = 1.11089
so, an effective rate of about 11%
To find the effective interest rate earned on the scheme, we need to calculate the future value including the bonus and then calculate the effective interest rate.
First, let's calculate the future value of the fixed deposit account after three years. The formula for compound interest is:
Future Value = Principal Amount * (1 + Interest Rate)^Number of Periods
In this case, the Principal Amount is 1 (since we are not given any specific value) and the Interest Rate is 10% per annum. The Number of Periods is 3 years.
So, the future value after three years will be:
Future Value = 1 * (1 + 0.10)^3
= 1.331
Now, let's calculate the bonus. The bonus is 3% of the final amount, which is 3% of 1.331. Therefore, the bonus amount will be:
Bonus Amount = 1.331 * 0.03
= 0.03993 (rounded to 4 decimal places)
Now, let's add the bonus amount to the final amount:
Final Amount = Future Value + Bonus Amount
= 1.331 + 0.03993
= 1.37093 (rounded to 5 decimal places)
Finally, to find the effective interest rate, we need to calculate the rate that will give us a future value of 1.37093 in three years.
Effective Interest Rate = (Final Amount / Principal Amount)^(1 / Number of Periods) - 1
= (1.37093 / 1)^(1 / 3) - 1
≈ 0.121 (rounded to 3 decimal places)
Therefore, the effective interest rate that will be earned on this scheme is approximately 12.1%.
To find the effective interest rate earned on this scheme, we need to consider both the annual interest rate and the bonus. Here's how to calculate it:
1. Calculate the amount after three years using compound interest formula:
A = P(1 + r/n)^(nt),
where A is the final amount, P is the principal (initial deposit), r is the annual interest rate (10% in this case), n is the number of times the interest is compounded per year (annually in this case), and t is the number of years (3 in this case).
A = P(1 + 0.10/1)^(1*3)
A = P(1 + 0.10)^3
A = P(1.10)^3
A = 1.331P
2. Calculate the bonus amount:
Bonus = 3% of the final amount
Bonus = 0.03 * A
Bonus = 0.03 * 1.331P
Bonus = 0.03993P
3. Calculate the total amount including the bonus:
Total amount = A + Bonus
Total amount = 1.331P + 0.03993P
Total amount = 1.37093P
4. Calculate the effective interest rate:
Effective interest rate = (Total amount - Principal) / Principal * 100
Effective interest rate = (1.37093P - P) / P * 100
Effective interest rate = 0.37093P / P * 100
Effective interest rate = 37.093%
Therefore, the effective interest rate earned on this scheme is 37.093%.