At the time of her grandson's birth, a grandmother deposits $ 3000 in an account that pays 3 % compounded monthly. What will be the value of the account at the child's twenty-first birthday, assuming that no other deposits or withdrawals are made during this period?
The value of the account will be $=

(Round to the nearest dollar as needed.)

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calculista calculista · Answer 1 · 2019-10-22T17:36:38+02:00

Answer:

The value of the account will be $5,628

Step-by-step explanation:

we know that

The compound interest formula is equal to

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

where

A is the Final Investment Value

P is the Principal amount of money to be invested

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

in this problem we have

[tex]t=21\ years\\ P=\$3,000\\ r=3\%=3/100=0.03\\n=12[/tex]

substitute in the formula above

[tex]A=3,000(1+\frac{0.03}{12})^{12*21}[/tex]

[tex]A=3,000(1.0025)^{252}[/tex]

[tex]A=\$5,628[/tex]

therefore

The value of the account will be $5,628