Question

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

Answer 1

(a)
`A=1600(1+(0.0375)/(12))^(12t)`

(where
`A` is the account balance and
`t` is the time in years)

(b) $1,929.40

Explanation:

Compound interest formula

`A=P(1+(r)/(n))^(nt)`

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:

`\implies A=1600(1+(0.0375)/(12))^(12t)`

(where
`A` is the account balance and
`t` is the time in years)

Part (b)

Substitute
`t=5` into the equation created in part (a):

`\implies A=1600(1+(0.0375)/(12))^(12\cdot 5)`

`\implies A=1600(1.003125)^(60)`

`\implies A=1929.404236...`

`\implies A=1929.40`

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