Question

KFind the future value and interest earned if $8806.54 is invested for 7 years at 4% compounded (a) semiannually and (b) continuously.(a) The future value when interest is compounded semiannually is approximately $ 11,620.04.(Type an integer or decimal rounded to the nearest hundredth as needed.)The interest earned is approximately $ 2813.5.(Type an integer or decimal rounded to the nearest hundredth as needed.)(b) The future value when interest is compounded continuously is approximately $(Type an integer or decimal rounded to the nearest hundredth as needed.)

Answer 1

Given:

The principal amount = $8806.54

Rate of interest = 4%

Time = 7 years

Required:

Find the future value when interest is compounded continuously.

Step-by-step explanation:

The future value is calculated by using the formula:

`Future\text{ value = Ae}^(rt)`

Where A = amount

r = rate of interest

t = time period

Substitute the given values in the formula:

`\begin{gathered} Future\text{ value = 8806.54\lparen e}^(0.04*7)) \\ =8806.54(e^(0.28)) \\ =8806.54*1.323 \\ =11,651.0524 \\ \approx11,651.05 \end{gathered}`

Interest = 11,651.05 - 8806.54

= 2844.51

Final Answer:

The future value when interest is compounded continuously is approximately $11,651.05.

The earned interest is approximately $2844.51