Respuesta :
Compounded annually:
The amount in the bank after 9 years is $7353.84
Compounded quarterly:
The amount in the bank after 9 years is $7469.63
Compounded monthly:
The amount in the bank after 9 years is $7496.71
Compounded continuously:
The amount in the bank after 9 years is $7510.44
Step-by-step explanation:
The formula of compounded interest including the principal sum is:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex] , where
- A is the future value of the investment/loan, including interest
- P is the principal investment amount
- r is the annual interest rate (decimal)
- n is the number of times that interest is compounded per unit t
- t is the time the money is invested or borrowed for
The formula of compound continuous interest is
[tex]A=Pe^{rt}[/tex] , where
- A is the future value of the investment, including interest
- P is the principal investment amount (the initial amount)
- r is the interest rate in decimal
- t is the time the money is invested for
∵ $4000 is invested in a bank account at an interest rate of
7 per cent per year
∴ P = 4000
∴ r = 7% = 7 ÷ 100 = 0.07
∵ The money is invested for 9 years
∴ t = 9
∵ The interest is compounded annually
∴ n = 1
- Substitute P, r, t and n in the 1st formula above
∴ [tex]A=4000(1+\frac{0.07}{1})^{(1)(9)}[/tex]
∴ A = 7353.84
The amount in the bank after 9 years is $7353.84
∵ The interest is compounded quarterly
∴ n = 4
- Substitute P, r, t and n in the 1st formula above
∴ [tex]A=4000(1+\frac{0.07}{4})^{(4)(9)}[/tex]
∴ A = 7469.63
The amount in the bank after 9 years is $7469.63
∵ The interest is compounded monthly
∴ n = 12
- Substitute P, r, t and n in the 1st formula above
∴ [tex]A=4000(1+\frac{0.07}{12})^{(12)(9)}[/tex]
∴ A = 7496.71
The amount in the bank after 9 years is $7496.71
∵ The interest is compounded continuously
- Substitute P, r, and t in the 2nd formula above
∴ [tex]A=4000e^{(0.07)(9)}[/tex]
∴ A = 7510.44
The amount in the bank after 9 years is $7510.44
Learn more:
You can learn more about compounded interest in brainly.com/question/2768526
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