Question 86995
#8

a)

Let p=7500, r=0.045, n=1, and t=19 and plug them into  {{{A=p(1+r/n)^(n*t)}}}


{{{A=7500(1+0.045/1)^(1*19)}}}       Start with the given expression
{{{A=7500(1+0.045)^(1*19)}}}     Divide 0.045 by 1 to get 0.045
{{{A=7500(1+0.045)^(19)}}}     Multiply the exponents 1 and 19 to get 19 
{{{A=7500(1.045)^(19)}}}       Add 1 and 0.045 to get 1.045
{{{A=7500(2.30786031084919)}}}      Raise 1.045 to the 19 th power to get 2.30786031084919
{{{A=17308.9523313689}}}       Multiply 7500 and 2.30786031084919 to get 17308.9523313689


So the return is $17,308.95


b)


Let p=600, r=0.045, n=12, and t=19 and plug them into  {{{A=p(1+r/n)^(n*t)}}}


{{{A=600(1+0.045/12)^(12*19)}}}       Start with the given expression
{{{A=600(1+0.00375)^(12*19)}}}     Divide 0.045 by 12 to get 0.00375
{{{A=600(1+0.00375)^(228)}}}     Multiply the exponents 12 and 19 to get 228 
{{{A=600(1.00375)^(228)}}}       Add 1 and 0.00375 to get 1.00375
{{{A=600(2.3476172358424)}}}      Raise 1.00375 to the 228 th power to get 2.3476172358424
{{{A=1408.57034150544}}}       Multiply 600 and 2.3476172358424 to get 1408.57034150544


So the return is $1408.57



So the $7,500 investment is larger after 19 years


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#9

To calculate the monthly payment, use this formula:


{{{Monthly_Payment=(P*R/(1-(1+R)^(-n)))}}} where P is the principal (i.e. the amount loaned out), R is the periodic interest rate (in decimal form) and n is the number of monthly payments


First lets calculate R:


{{{R=10.8/(12*100)=0.009}}} To find the periodic interest rate, divide the APR (this is given as 10.8%) by the number of months in a year. Also divide the APR by 100 to convert the percentage to a decimal






{{{Monthly_Payment=(26000*0.009/(1-(1+0.009)^(-15*12)))}}} Start with the given expression


{{{Monthly_Payment=(26000*0.009/(1-(1.009)^(-15*12)))}}} Add {{{1+0.009}}} to get 1.009


{{{Monthly_Payment=(26000*0.009/(1-(1.009)^(-180)))}}} Multiply {{{-15*12}}} to get -180


{{{Monthly_Payment=(26000*0.009/(1-(0.199337991176801)))}}} Raise 1.009 to the -180 power


{{{Monthly_Payment=(26000*0.009/(0.800662008823199)))}}} Subtract {{{1-0.199337991176801}}} to get 0.800662008823199


{{{Monthly_Payment=(234/(0.800662008823199)))}}} Multiply {{{26000*0.009}}} to get 234


{{{Monthly_Payment=(292.258153154949)))}}} Divide 234 by 0.800662008823199 to get 292.258153154949



So the monthly payment, rounded to the nearest cent, is roughly $292.26