Question

A $40,000 is placed in a scholarship fund that earns an annual interest rate of 4.25% compounded daily find the value in dollars of the account after 2 years assume years have 365 days round your answer to the nearest cent

Answer 1

From the question, we want to find the value in dollars of the account after 2 years.

We will usethe formula

`\begin{gathered} A=P(1+(r)/(n))^(nt) \\ Where\text{ A = value of the account, amount in dollars = ?} \\ P=principal\text{ money invested = 40,000 dollars } \\ r=annual\text{ interest rate = 4.25\% = }(4.25)/(100)=0.0425 \\ n=number\text{ of times compounded = daily = 365} \\ t=time\text{ in years = 2 years } \end{gathered}`

Applying this, we have

`\begin{gathered} A=P(1+(r)/(n))^(nt) \\ A=40,000(1+(0.0425)/(365))^(365*2) \\ A=40,000(1.000116438)^(730) \\ A=40,000*1.0887116 \\ A=43,548.467179 \\ A=43,548.47\text{ dollars } \end{gathered}`

Hence the answer is 43,548.47 to the nearest cent