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

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