Capital Value Suppose income from an investment starts (at time 0) at $6000 a year and increases linearly and continuously at a rate of $200 a year. Find the capital value at an interest rate of 5% compounded continuously.

When an amount is compounded continuously interest it means the principal is continuously earning interest and the interest keeps earning on the interest earned. The formula to apply is;

[tex]A=Pe^{rt}[/tex]

where P is the starting amount, r is the nominal annual interest rate, t is length of time the interest is applied, and e=2.71828

Given that, A=$6000, e=2.71828, r=0.05 and t=1

[tex]A=6000*2.71828^{0.05}[/tex]

A=6307.63

Interest earned= 6307.63-6000 = $307.63

Where the investment increases linearly and at a constant rate of $200 a per , the linear model will be;

A=6000+200t where t is length of time the interest is applied, and A is the amount after t period of time

In this case t=1

A=6000+200*1

A=6000+200 =6200

Interest earned is= $6200-$6000=$200

Capital value = $6000+$307.63+$200 =$6507.63

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Interest compounded continuously:https://brainly.com/question/13009340

Keywords : capital value, investment, increases linearly, continuously rate

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