Question

Martina invested 4900 in an account that pays an annual interest rebate of 2.6%, compounded daily. Assume there are 365 days in each year. Answer each part

Answer 1

Given:

Principal P = $4900

Interest rate = 2.6%

Required:

(1) Find the amount after one year when the interest is compounded daily.

(2) Find the effective annual interest.

Step-by-step explanation:

(1) The amount formula when the interest is compounded daily is given as:

`A=P(1+(r)/(n))^(nt)`

Where A = amount

P =Principal

r = rate of interest

n= compounde time

t = time in years

substitute the given values.

`\begin{gathered} A=4900(1+(0.026)/(365))^(365*1) \\ A=4900(1+0.0000712)^(365) \\ A=4900*1.0263399 \\ A=5029.065 \\ A\approx5029.07 \end{gathered}`

Thus the amount after 1 year is $5209.07

(2) The effective annual interest rate is given by the formula:

`EAR=\text{ \lparen1+}(i)/(n))^n-1`

Where i = interest rate

n = compounding time

`\begin{gathered} EAR=(1+(0.026)/(365))^(365)-1 \\ =1.0263399-1 \\ =0.0263399 \end{gathered}`

Thus the effective annual interest rate is 2.63%

Final Answer:

(1) The amount after one year when the interest is compounded daily is $5209.07

(2) The effective annual interest is 2.63%