Question

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.

Answer 1

The capital value$6507.63

Step-by-step explanation:

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;

$A=Pe^{rt}$

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

$A=6000*2.71828^{0.05}$

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:brainly.com/question/13009340

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

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