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A bank features a savings account that has an annual percentage rate of r=5.2% with interest compounded quarterly. Marcus deposits $8,500 into the account.

The account balance can be modeled by the exponential formula S(t)=P(1+rn)^nt, where S is the future value, P is the present value, r is the annual percentage rate written as a decimal, n is the number of times each year that the interest is compounded, and t is the time in years.

(A) What values should be used for P, r, and n?

P= _____ , r=______ , n=________

(B) How much money will Marcus have in the account in 7 years?
Answer = $______ .
Round answer to the nearest penny.

Respuesta :

calculista

Answer:

Part A)

[tex]P=\$8,500\\ r=0.052\\n=4[/tex]  

Part B) [tex]S(7)=\$12,203.47[/tex]  

Step-by-step explanation:

we know that    

The compound interest formula is equal to  

[tex]S(t)=P(1+\frac{r}{n})^{nt}[/tex]  

where  

S is the Future Value  

P is the Present Value  

r is the rate of interest  in decimal

t is Number of Time Periods  

n is the number of times interest is compounded per year

Part A)

in this problem we have  

[tex]P=\$8,500\\ r=5.2\%=5.2/100=0.052\\n=4[/tex]  

Part B) How much money will Marcus have in the account in 7 years?

we have

[tex]t=7\ years\\ P=\$8,500\\ r=0.052\\n=4[/tex]  

substitute in the formula above  

[tex]S(7)=8,500(1+\frac{0.052}{4})^{4*7}[/tex]  

[tex]S(7)=8,500(1.013)^{28}[/tex]  

[tex]S(7)=\$12,203.47[/tex]  

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