Final answer:
To find the total amount of interest after 16 years at an annual interest rate of 2.5% compounded annually, use the compound interest formula. The total amount of interest after 16 years will be $1490.68. To calculate the total amount repaid after 7 months with an interest rate of 11%, use the simple interest formula. The total amount repaid would be $4266.67.
Step-by-step explanation:
To find the total amount of interest on Sumi Kato's savings account after 16 years at an annual interest rate of 2.5% compounded annually, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
- A = future amount (including principal and interest)
- P = principal (initial amount)
- r = annual interest rate (as a decimal)
- n = number of times the interest is compounded per year
- t = number of years
Given that Sumi Kato's savings account has a balance of $3394, we can substitute the values into the formula:
A = 3394(1 + 0.025/1)^(1 * 16)
A = 3394(1.025)^16
A ≈ 3394(1.4371)
A ≈ $4884.68
Therefore, the amount of interest after 16 years will be approximately $4884.68 - $3394 = $1490.68.
For Allan's loan, to calculate the total amount he repaid after 7 months with an interest rate of 11% per year, we can use the formula for simple interest:
I = P * r * t
Where:
- I = interest amount
- P = principal amount
- r = annual interest rate (as a decimal)
- t = time (in years)
Given that Allan borrowed $4000, we can substitute the values into the formula:
I = 4000 * 0.11 * (7/12)
I ≈ 266.67
Therefore, the total amount he repaid would be $4000 + $266.67 = $4266.67.