SOLUTION: 2.) Compound interest. Suppose that $750 is invested at 7% interest, compounded semiannually. A.) Find the function for the amount to which the investment grows after t years.

Algebra ->  Graphs -> SOLUTION: 2.) Compound interest. Suppose that $750 is invested at 7% interest, compounded semiannually. A.) Find the function for the amount to which the investment grows after t years.      Log On


   

Question 149830: 2.) Compound interest. Suppose that $750 is invested at 7% interest, compounded semiannually.
A.) Find the function for the amount to which the investment grows after t years.
B.)Find the amount of money in the account at t=1, 6,10,15, and 25 yr
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
A)
The compound interest formula is A=P%281%2Br%2Fn%29%5E%28nt%29 where A is the return, P is the principal, r is the interest rate, n is the compound frequency, and t is the time in years.


So in this case, the principal is P=750, the rate is r=0.07 (note 7% is 0.07 in decimal form) and the compound frequency is n=2 (note: semiannually means that it is compounded twice a year)

So the equation is A=750%281%2B0.07%2F2%29%5E%282t%29

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B)

Let's find out how much money there is in the account after 1 year


A=750%281%2B0.07%2F2%29%5E%282%2At%29 Start with given equation


A=750%281%2B0.07%2F2%29%5E%282%2A1%29 Plug in t=1


A=750%281%2B0.035%29%5E%282%2A1%29 Divide 0.07 by 2 to get 0.035


A=750%281%2B0.035%29%5E%282%29 Multiply the exponents 2 and 1 to get 2


A=750%281.035%29%5E%282%29 Add 1 and 0.035 to get 1.035


A=750%281.071225%29 Raise 1.035 to the 2 th power to get 1.071225


A=803.41875 Multiply 750 and 1.071225 to get 803.41875


So in 1 year, there is $803.42 (rounded to the nearest cent) in the account

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Let's find out how much money there is in the account after 6 years


A=750%281%2B0.07%2F2%29%5E%282%2At%29 Start with given equation.


A=750%281%2B0.07%2F2%29%5E%282%2A6%29 Plug in t=6


A=750%281%2B0.035%29%5E%282%2A6%29 Divide 0.07 by 2 to get 0.035


A=750%281%2B0.035%29%5E%2812%29 Multiply the exponents 2 and 6 to get 12


A=750%281.035%29%5E%2812%29 Add 1 and 0.035 to get 1.035


A=750%281.51106865734636%29 Raise 1.035 to the 12 th power to get 1.51106865734636


A=1133.30149300977 Multiply 750 and 1.51106865734636 to get 1133.30149300977


So in 6 years, there is $1133.30 (rounded to the nearest cent) in the account



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Let's find out how much money there is in the account after 10 years


A=750%281%2B0.07%2F2%29%5E%282%2At%29 Start with given equation.


A=750%281%2B0.07%2F2%29%5E%282%2A10%29 Plug in t=10


A=750%281%2B0.035%29%5E%282%2A10%29 Divide 0.07 by 2 to get 0.035


A=750%281%2B0.035%29%5E%2820%29 Multiply the exponents 2 and 10 to get 20


A=750%281.035%29%5E%2820%29 Add 1 and 0.035 to get 1.035


A=750%281.98978886346584%29 Raise 1.035 to the 20 th power to get 1.98978886346584


A=1492.34164759938 Multiply 750 and 1.98978886346584 to get 1492.34164759938



So in 10 years, there is $1492.34 (rounded to the nearest cent) in the account

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Let's find out how much money there is in the account after 15 years


A=750%281%2B0.07%2F2%29%5E%282%2At%29 Start with given equation.


A=750%281%2B0.07%2F2%29%5E%282%2A15%29 Plug in t=15


A=750%281%2B0.035%29%5E%282%2A15%29 Divide 0.07 by 2 to get 0.035


A=750%281%2B0.035%29%5E%2830%29 Multiply the exponents 2 and 15 to get 30


A=750%281.035%29%5E%2830%29 Add 1 and 0.035 to get 1.035


A=750%282.80679370470263%29 Raise 1.035 to the 30 th power to get 2.80679370470263


A=2105.09527852697 Multiply 750 and 2.80679370470263 to get 2105.09527852697


So in 15 years, there is $2105.10 (rounded to the nearest cent) in the account

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Let's find out how much money there is in the account after 15 years


A=750%281%2B0.07%2F2%29%5E%282%2At%29 Start with given equation.


A=750%281%2B0.07%2F2%29%5E%282%2A25%29 Plug in t=25


A=750%281%2B0.035%29%5E%282%2A25%29 Divide 0.07 by 2 to get 0.035


A=750%281%2B0.035%29%5E%2850%29 Multiply the exponents 2 and 25 to get 50


A=750%281.035%29%5E%2850%29 Add 1 and 0.035 to get 1.035


A=750%285.58492685566332%29 Raise 1.035 to the 50 th power to get 5.58492685566332


A=4188.69514174749 Multiply 750 and 5.58492685566332 to get 4188.69514174749



So in 25 years, there is $4188.69 (rounded to the nearest cent) in the account