Question

Calculate the future value of $76,010.00, earning interest at a rate of 2 1/5% of that is compounded daily for 2 years.$76,010.00$79,429.00$6,109,851.09$778,342.40

Answer 1

Given;

`\begin{gathered} Principal(P)=76010.00 \\ rate(r)=2(1)/(5)\%=(11)/(5)\%=2.2\%=0.022 \end{gathered}`

To Determine: The future value after 2 years if the compounded daily

Solution:

The future value of a compound interest is calculated using the formula

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

`\begin{gathered} Where \\ A=Future\text{ value} \\ P=Principal(amount\text{ invested\rparen} \\ r=rate \\ n=365\text{ for daily compounds\rparen} \\ t=time\text{ in years} \end{gathered}`

Substitute the given into the formula

`\begin{gathered} A=76010(1+(0.022)/(365))^(365*2) \\ A=76010(1+0.00006027397)^(730) \end{gathered}`

`\begin{gathered} A=76010(1.00006027397)^(730) \\ A=79429.00 \end{gathered}`

Hence, the future value is $79,429.00