Question

Your grandparents deposit $2,000 each year on your birthday, starting the day you are born, in an account that pays 7% interest compounded annually. How much will you have in the account on your 21st birthday, just after your grandparents make their deposit

Answer 1

Answer:

The money you will have is $98020.

Explanation:

It is given that grandparents deposit $2,000 each year on birthday and the account pays 7% interest compounded annually also the time is 21 years.

we will use the compound interest formula  $A=P (1 + \frac{r}{100})^{t}$.

For the first birthday the amount after 21 yr will be:

$A=2000(1+\frac{7}{100})^{21}$

Similarly for the second birthday amount after 20yr will be:

$A=2000(1+\frac{7}{100})^{20}$

likewise, the last compound will be:

$A=2000(1+\frac{7}{100})^1$

The total value of such compounding would be :

$\text {Total amount}=2000(1+\frac{7}{100})^{21}+2000(1+\frac{7}{100})^{20}...2000(1+\frac{7}{100})^{1}$

$\text {Total amount}=2000[(1+\frac{7}{100})^{21}+(1+\frac{7}{100})^{20}...(1+\frac{7}{100})^{1}]$

$\text{Total amount} \approx 2000(48.01)$

$\text{Total amount} \approx 96020$

The total amount just after your grandparents make their​ deposit  is:

≈($96020+2000)

≈$98020

Hence, the money you will have is $98020.