Question

Tony saved enough money to place $125,500 in an investment generating 9.25% compounded monthly. He wants to collect a monthly income of $1,350, at the beginning of each month, for as long as the money lasts. How many months will Tony have this income coming to him?

Answer 1

Answer:

It will last for 161.70 months

Explanation:

we need to solve for n in an annuity-due

$C \times \frac{1-(1+r)^{-time} }{rate} (1+rate)= PV$  

C  $1,350.00  

time n

rate 9.25% annual -->0.0925/ 12 = 0.007708333

PV $125,500.0000  

$1350 \times \frac{1-(1+0.0077083)^{-n} }{0.0077083} (1+0.00770833)= 125500$  

$(1+0.0077083)^{-n}= 1-\frac{125500\times0.0077083}{1350}(1.00770833)$  

$(1+0.0077083)^{-n}= 0.29  $

[tex]-n= \frac{log0.288891951699477}{log(1+0.0077083)  

-n = -161.7057904

n = 161.7057