190k views
3 votes
$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.

1 Answer

0 votes

Answer


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}

User Gstukelj
by
8.5k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories