Respuesta :
Answer:
a) [tex]A(t) = 77000(1.01375)^{4t}[/tex]
b)
The amount of money in the account at t = 0 years is $77,000.
The amount of money in the account at t = 3 years is $90,711.
The amount of money in the account at t = 6 years is $106,864.
The amount of money in the account at t = 10 years is $132,961.
Step-by-step explanation:
The compound interest formula is given by:
[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]
Where A(t) is the amount of money after t years, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per unit t and t is the time the money is invested or borrowed for.
Suppose that $77,000 is invested at 5 1/2% interest, compounded quarterly.
This means that, respectively, [tex]P = 77000, r = 0.055, n = 4[/tex]
a) Find the function for the amount to which the investment grows after t years.
[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]
[tex]A(t) = 77000(1 + \frac{0.055}{4})^{4t}[/tex]
[tex]A(t) = 77000(1.01375)^{4t}[/tex]
b) Find the amount of money in the account at t=0,3, 6, and 10 years.
[tex]A(0) = 77000(1.01375)^{4*0} = 77000[/tex]
The amount of money in the account at t = 0 years is $77,000.
[tex]A(3) = 77000(1.01375)^{4*3} = 90711[/tex]
The amount of money in the account at t = 3 years is $90,711.
[tex]A(6) = 77000(1.01375)^{4*6} = 106864[/tex]
The amount of money in the account at t = 6 years is $106,864.
[tex]A(10) = 77000(1.01375)^{4*10} = 132961[/tex]
The amount of money in the account at t = 10 years is $132,961.
