Find the effective interest rate r_{e} for investments with the following annual int

Tabansi

Tabansi

Answered question

2021-08-12

Find the effective interest rate re for investments with the following annual interest rates.
Express your answer as a percentage, rounded to 2 decimals, and without the sign (e.g., 8.79)
a) 3.55% compounded monthly
b) 3.53% compounded daily (using 365 days per year).
c) 3.49% compounded continuously

Answer & Explanation

Tuthornt

Tuthornt

Skilled2021-08-13Added 107 answers

Step 1
Here we have to find the effective interest rate for investment with the following interest rate,
So, we will use the following formula,
re=(1+rn)n1
Or, re=er1
Here it is depending on if the interest is compounded n times per year or continuously.
Step 2
a) 3.55% compounded monthly
So, here we use the formula, re=(1rn)n1
Where, r=0.0355 and n=12
So, re=(1+0.035512)121
re=(1.002958)121
re=0.03608
Hence, the effective interest rate is about 3.61%
Step 3
b) 3.53% compounded daily (using 365 days per year).
Using the formula, re=(1+rn)n1
Where, r=0.0353 and n=365
So, re=(1+0.0353365)3651
re=0.03592
Hence, the effective interest rate is about 3.59%
Step 4
c) 3.49% compounded continuously
Here, we are using the formula re=er1
Where, r=0.0349
re=e0.03491
re=0.03551
Hence, the effective interest rate is about 3.55%

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