# Math

posted by
**Natalie** on
.

Your Aunt will give your $1,ooo if you invest it for 10 years in an account that pays 20% interest compounded annually. That is, at the end end of each year your interest will be added to your account and invested at 20%.

What will your account be worth at the end of 10 years? How much interest will you earn during the 10t year?

(1+.20)10? I am stuck!

Ok, do you know the formula

A=P(1+r)^n ?

Where A is the amount earned, P is the principal (which is 1,000), r is the rate expressed as a decimal (.20 here), and n is the number of years.

Your formula, "(1+.20)10" is missing the exponential sign. It should be (1+.02)^10 which is approx. 6.1917364224.

Therefore if the principal is 1,000 then A is 1,000*6.1917364224 = approx. $6,192.

To calculate the amount earned in the 10th year, determine what the amount would have been after 9 years and subtract that from the amount above.

Let us know if you need further help or want to verify answers.

plan and solve

You can use S = P(1 + i)^n to determine the accumulated amount at the end of each year where P is the invested amount, i is the decimal equivalant of the interest rate per interest bearing period, n is the number of interst paying periods in a year and S is the accul;ated sum.

Therefore. S = 1000(1 + .2)^10 = $6,191.73.

The value after 9 years would be $5,159.78.

Therefore the interest gained in the 10th year would e the difference of the two results or $1031.95.