Question

$1,400 is invested in an account earning 4.3% interest (APR), compounded daily.Write a function showing the value of the account after t years, where the annualgrowth rate can be found from a constant in the function. Round all coefficients inthe function to four decimal places. Also, determine the percentage of growth peryear (APY), to the nearest hundredth of a percent.

Answer 1

`A=1400(1.0001)^(365t)`

APY = 4.39 %

Explanation

Compound interest formula

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

where

• A: final amount (value of the account after t years)

,

• P: principal (amount of money invested)

,

• r: interest rate (APR), as a decimal

,

• n: number of times interest applied per year

,

• t: time in years

Substituting, P = $1400, r = 0.043 (= 4.3/100), n = 365 (compounded daily means 365 times per year), we get:

`\begin{gathered} A=1400(1+(0.043)/(365))^(365t) \\ A=1400(1.0001)^(365t) \end{gathered}`

APY formula

`APY=\lbrack(1+(r)/(n))^n-1\rbrack*100`

Substituting with the before mentioned values, we get:

`\begin{gathered} APY=\lbrack(1+(0.043)/(365))^(365)-1\rbrack*100 \\ APY=4.39\text{ \%} \end{gathered}`