4 (5a²b³) ^2 / (2x³y^5) 4 show your work

You invest $15,000 in a savings account with an annual interest rate of 2.5% in which the interest is compounded quarterly. How much money should you expect to have in the account after 5 years? Show your work

Step-by-step explanation:

1) 4 (5a²b³) ^2 / (2x³y^5) 4

Opening the parenthesis in the denominator, it becomes

4 (5a²b³) ^2 / 8x³y^5

Recall: (b^x) ^y = b ^ (xy)

It becomes

4 (5^2a^4b^6) / 8x³y^5

4*25a^4b^6) / 8x³y^5

= 100a^4b^6) / 8x³y^5

2) Initial amount invested into the account is $15000 This means that the principal is P, so

P = 15000

It was compounded quarterly. This means that it was compounded 4 times in a year. So

n = 4

The rate at which the principal was compounded is 2.5%. So

r = 2.5/100 = 0.025

It was compounded for 5 years. So

t = 5

The formula for compound interest is

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

A = total amount in the account at the end of t years. Therefore

A = 15000 (1+0.025/4) ^4*5

A = 15000 (1+0.00625) ^20

A = 15000 (1.00625) ^20

A = 16990.62

Approximately $16991