Question

At the time of her​ grandson's birth, a grandmother deposits $ 5000 in an account that pays 2 % 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?

Answer 1

The value of account will be $7607.15 at the child's 21st birthday.

Explanation:

The formula of compound interest:

`A=P(1+\frac rn)^(nt)`

A= Amount after t years

P= Initial amount.

r = rate of interest

n= Number of interest pay in a year.

Given that, a grandmother deposit $5000 in an account that pay 2% compounded monthly at the time of her grandson's birth,.

Here P= $5000, r= 2%=0.02, n=12 and t= 21 years.

`A=P(1+\frac rn)^(nt)`

`\Rightarrow A=5000(1+(0.02)/(12))^(12* 21)`

≈$7607.15

The value of account will be $7607.15 at the child's 21st birthday.