Reggie

2020-10-26

Calculate the value and interest that would be earned if \$56,780 is invested at $2.8\mathrm{%}$ compounded a) quarterly for 23 quarters b) continuosly for 15 year

joshyoung05M

Given, Present value, interest rate and time in quarterly are
$PV=\mathrm{}56780$

$t=23$ quarterly
Part (a): The formula for Future value and interest are
$FV=PV{\left(1+r\right)}^{t}\phantom{\rule{1em}{0ex}}\text{and}\phantom{\rule{1em}{0ex}}IFV-PV$
$PV=$ Present value
$FV=$ Future value
$I=$ Interest
$r=$ rate quarterly
$t=$ time in quarterly
The Amount is
$FV=\mathrm{}56780{\left(1+0.028\right)}^{23}$
$=\mathrm{}56780{\left(1.028\right)}^{23}$
$=\mathrm{}56780\left(1.88730303\right)$
$=\mathrm{}107161.066$
$I=\mathrm{}107161.066-56780$
$=\mathrm{}50381.066$
Part (b): The formula for Future value and interest are
$FV=PV\cdot {e}^{n}\phantom{\rule{1em}{0ex}}\text{and}\phantom{\rule{1em}{0ex}}I=FV-PV$
$PV=$ Present value
$FV=$ Future value
$I=$ Interest
$r=$ rate
$t=$ time in years
The amount is
$FV=\mathrm{}56780\cdot {e}^{0.028\left(15\right)}$
$=\mathrm{}56780\cdot \left(1.521961556\right)$
$=\mathrm{}86416.97713$
$I=\mathrm{}86416.97713-56780$
$=\mathrm{}29636.97713$

Jeffrey Jordon