Respuesta :
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 [tex]A=P (1 + \frac{r}{100})^{t}[/tex].
For the first birthday the amount after 21 yr will be:
[tex]A=2000(1+\frac{7}{100})^{21}[/tex]
Similarly for the second birthday amount after 20yr will be:
[tex]A=2000(1+\frac{7}{100})^{20}[/tex]
likewise, the last compound will be:
[tex]A=2000(1+\frac{7}{100})^1[/tex]
The total value of such compounding would be :
[tex]\text {Total amount}=2000(1+\frac{7}{100})^{21}+2000(1+\frac{7}{100})^{20}...2000(1+\frac{7}{100})^{1}[/tex]
[tex]\text {Total amount}=2000[(1+\frac{7}{100})^{21}+(1+\frac{7}{100})^{20}...(1+\frac{7}{100})^{1}][/tex]
[tex]\text{Total amount} \approx 2000(48.01)[/tex]
[tex]\text{Total amount} \approx 96020[/tex]
The total amount just after your grandparents make their deposit is:
≈($96020+2000)
≈$98020
Hence, the money you will have is $98020.
