Suppose you borrow at the risk-free rate an amount equal to your initial wealth and invest in a portfolio with an expected retur
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Answer:
You will receive $201.38 more interest if the investment is made with a compound interest rate rather than a simple interest rate.
Explanation:
<u>Simple interest rate</u>
We can calculate how much interests you'd obtain if you deposited the $2,600 in a simple interest rate account.
We start using the following formula for calculating the simple interests:
Where:
<em>I</em> are the interests per year,
<em>P</em> is the amount being invested,
<em>r</em> is the interest rate.
Replacing in the formula with the given values we have:
We then proceed to multiply this result by the <em>given number of years</em>, which is 8. We get .
Finishing with the <em>simple interest rate</em>, if we wanted to know how much is the investment worth at the end of a 8 year period, we must merely add <em>the principal</em> (the $2,600) to the total interests after the end of the period ($1040). So .
We'll use these results later.
<u>Compound interest rate</u>
The formula for compound interests is the following:
Where:
<em>I</em> is the value of the investment after <em>n</em> years,
<em>P</em> is the principal amount being invested,
<em>r</em> is the interest rate,
<em>n</em> are the number of years the investment is compounded.
Replacing in the formula with the given values we have:
After the 8 year period, the investor will have $3841.38 in it's compounded interest account.
<u>Comparing these results</u>
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We can simply substract the value of both investments at the end of a 8 year period, to determine how much more interest does the compound interest rate account give in relation to a simple interest rate account.
The values we've gotten were:
$3,640 for the simple interest rate account, and
$3,841.38 for the compounded interest rate account.
. Therefore the answer is: the account that pays compounded interests will pay $201.38 more to this invididual, compared to an account that pays simple interest.