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Sidana [21]
3 years ago
12

You can invest in an account that pays simple interest or an account that pays compound interest. In either case, you plan to in

vest $2,600 today and both accounts have an annual interest rate of 5 percent. How much more interest will you receive in the 8th year in the account that pays compound interest?
Business
1 answer:
trasher [3.6K]3 years ago
8 0

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:

I=P * r

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:

I=2600*0.05=130

We then proceed to multiply this result by the <em>given number of years</em>, which is 8. We get 130*8=1040.

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 2600+1040= 3640.

We'll use these results later.

<u>Compound interest rate</u>

The formula for compound interests is the following:

I=P(1+r)^n

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:

I=2600*(1+0.05)^8=3841.38

After the 8 year period, the investor will have $3841.38 in it's compounded interest account.

<u>Comparing these results</u>

<u></u>

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.

3841.38-3640=201.38. 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.

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The present value of the cash-flow stream if the interest rate is 6% is $323.03.

<h3>What is the interest rate?</h3>

The interest rate can be defined as the amount or the percentage that is being fixed or fluctuating depending upon the condition of the agreement. The interest is calculated on the amount that is being loaned or given to the individual or a company.

According to the given question, the interest rate is 6%

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Now, by applying the formula for the present value:

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