Which investment option will pay the most interest?
A. 12.6% compounded annually
B. 12.4% compounded semiannually
C. 12.2% compounded quarterly
D. 12.0% compounded continuously
E. These investments all pay the same amount of interest.
a) 1.126^1 =
b) (1.062)^2 =
c) (1.0305)^4 =
d) (e)^.12 =
Where did you get the values from?
Are you not studying compound interest?
e.g.
c) rate is 12.2 compounded quarterly,
so in (1+i)^n
i = .122/4 = .0305
n = 4
so (1+.0305)^4 = 1.0305)^4
To determine which investment option will pay the most interest, we need to compare the effective annual interest rates.
The effective annual interest rate accounts for the compounding frequency and allows for an accurate comparison between different compounding periods.
Option A has an interest rate of 12.6% compounded annually. This means that the interest is calculated once a year.
Option B has an interest rate of 12.4% compounded semiannually. This means that the interest is calculated twice a year.
Option C has an interest rate of 12.2% compounded quarterly. This means that the interest is calculated four times a year.
Option D has an interest rate of 12.0% compounded continuously. This means that the interest is calculated continuously throughout the year.
To compare these options, we need to calculate the effective annual interest rate.
For option A, the effective annual interest rate is 12.6%.
For option B, we can calculate the effective annual interest rate using the formula:
Effective Annual Interest Rate = (1 + (Interest Rate / Number of Compounding Periods))^Number of Compounding Periods - 1
Plugging in the values, we get:
Effective Annual Interest Rate = (1 + (0.124 / 2))^2 - 1 ≈ 0.12475 or 12.475%
For option C, we can use the same formula:
Effective Annual Interest Rate = (1 + (0.122 / 4))^4 - 1 ≈ 0.12415 or 12.415%
For option D, the effective annual interest rate for continuously compounded interest is equal to the stated interest rate. Therefore, the effective annual interest rate is 12.0%.
Comparing the effective annual interest rates, we find that option A (12.6% compounded annually) has the highest rate. Therefore, option A will pay the most interest.