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.

Question

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calculista calculista · Answer 1 · 2019-07-31T20:51:14+02:00

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]