Question

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

Answer 1

You will receive $201.38 more interest if the investment is made with a compound interest rate rather than a simple interest rate.

Step-by-step explanation:

Answer 2

You will receive $201.38 more interest if the investment is made with a compound interest rate rather than a simple interest rate.

Step-by-step explanation:

Simple interest rate

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:

I are the interests per year,

P is the amount being invested,

r 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 given number of years, which is 8. We get
`130*8=1040`.

Finishing with the simple interest rate, if we wanted to know how much is the investment worth at the end of a 8 year period, we must merely add the principal (the $2,600) to the total interests after the end of the period ($1040). So
`2600+1040= 3640`.

We'll use these results later.

Compound interest rate

The formula for compound interests is the following:

`I=P(1+r)^n`

Where:

I is the value of the investment after n years,

P is the principal amount being invested,

r is the interest rate,

n 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.

Comparing these results

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.