# Option 1 Invest $5,000 in a savings account at 6.6% interest compounded monthly. compound interest Option 1 amount earned at the end of 6 yearsIt is Business Algebra

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All you are trying to do here is to find what you get by investing at compound interest. The formula for compound interest is

A = P(1+r/n)^nt

In this formula, A is the amount of money you have after t years. P is the original amount of money invested, r is the annual interest rate expressed as a decimal and n is the number of times interest is compounded each year.

So now plug in the numbers that you have provided.

A = 5000(1+.066/12)^12*6

If you do the math correctly you will come out with $7421.29. So your original $5000 investment will become $7421.29, which means that you earned $2421.29 in interest during the 6 years.

A nominal annual 6.6% is equivalent to 6.6%/12 =0.55% monthly.

This is equivalent to the interest of $ 0.55/100 = $0.0055 per dollar per mont.

Therefore, by monthly compound interest, a principle of 1 dollar, along with 0.0055 monthly interest per dollar becomes,

$1.0055 in1st month, 1.055^2 in 2nd month, 1.0055^3, in 3r month, ..... and like that $1.0055^n in the nth month respectively alng with the interest under the compound interest principle.

In 6 years, there are 6*12 months and therefore, a dollar becomes $1.055^72 = $1.484257.

Therefore, in 6 years, $5000 brings 5000*1.055^72 = $7421.29.

So excleding the principle ,$5000, the interest earned is $(7421.29-5000) = $2421.29

Given:

Principle Amount = a = $5000

Compound interest rate = 6.6% per year = 0.55% per month = i

Compounding period = every month

Total duration of the deposit = 6 years = 72 months = n

Then the amount of principle plus interest at the end of the deposit period (n months) is given by

Total amount after n months = p*(1 + i/100)^n

= 5000*(1 + 0.55/100)^72

= 5000*(1.0055)^72

= 7421.29

Interest earned = Total amount - Principal amount

= 7421.29 - 5000 = 2421.29

Answer:

Compound interest earned is $2421.29.