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Mrs Galicia started a savings account for her family and started it with an initial deposit of $1600. The account earns 3.75% interest compounded quarterly.
(a) Write an equation to represent the amount of money in the account as a function of time in years.
(b) How much money will be present in the account in 5 years. **Must show plug in step before using calculator

Respuesta :

semsee45

Answer:

(a) [tex]A=1600(1+\frac{0.0375}{12})^{12t}[/tex]

     (where [tex]A[/tex] is the account balance and [tex]t[/tex] is the time in years)

(b) $1,929.40

Step-by-step explanation:

Compound interest formula

[tex]A=P(1+\frac{r}{n})^{nt}[/tex]

where:

  • A is the amount
  • P is the principal
  • r is the interest rate (in decimal form)
  • t is time
  • n is the number of times the interest is compounded per unit of t

Given:

  • P = $1600
  • r = 3.75% = 3.75/100 = 0.0375
  • t = number of years
  • n = 12 (as the interest is compounded monthly and t is number of years)

Substituting these values into the formula:

[tex]\implies A=1600(1+\frac{0.0375}{12})^{12t}[/tex]

(where [tex]A[/tex] is the account balance and [tex]t[/tex] is the time in years)

Part (b)

Substitute [tex]t=5[/tex] into the equation created in part (a):

[tex]\implies A=1600(1+\frac{0.0375}{12})^{12\cdot 5}[/tex]

[tex]\implies A=1600(1.003125)^{60}[/tex]

[tex]\implies A=1929.404236...[/tex]

[tex]\implies A=1929.40[/tex]

Therefore, her account balance after 5 years will be $1,929.40

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