Raj placed $8000 in saving account. For how long can $800 be withdrawn from the account at the end of every month starting one month from now if interest is 4.58% compounded monthly?

 

We've learned two formulas, I don't know how to alter them to calculate this.

?FV=PMT×(1+R)×(((1+R)n−1)/R)?

?PV=PMT×(1+R)×((1−(1+R)−n)/R)?

Please explain your answer Thank you :)

Time taken is approximately 13 months.

Step-by-step explanation

?PV=PMT×(1+R)×((1−(1+R)−n)/R)

$8000 = $800 x (1+4.58%)x((1−(1+4.58%)⁻ⁿ)/4.58%)

($8,000/$800) = (1.0458) x (1-1.0458^-n) / 0.0458

(10x0.0458)/1.0458 = (1-1.0458^-n)

(1-1.0458^-n)= 0.4379

1.0458^-n = (1-0.4379)

1.0458^-n = 0.5621

To solve for n, Log of the numbers is introduced on both sides of the equation,

Log 1 - Log 1.0458n = log 0.5621

(Log 1 - Log 0.5621) = n Log 1.0458

n = (Log 1 - Log 0.5621) / Log 1.0458

n = (0--0.2502) / 0.01945

n=(0.2502/0.01945)

n=12.86.

It will take approximately 13 months for the money to be withdrawn.