Question

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.)

Answer 1

The value of the account will be $5,628

Explanation:

we know that

The compound interest formula is equal to

`A=P(1+(r)/(n))^(nt)`

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

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

substitute in the formula above

`A=3,000(1+(0.03)/(12))^(12*21)`

`A=3,000(1.0025)^(252)`

`A=\$5,628`

therefore

The value of the account will be $5,628