SOLUTION: 1. Assume you invest $10,000 in a mutual fund (e.g. money market fund) at an APR of 7% compounded quarterly. How long, to the nearest tenth of a year, will it take the $10,000 to

Algebra ->  Finance -> SOLUTION: 1. Assume you invest $10,000 in a mutual fund (e.g. money market fund) at an APR of 7% compounded quarterly. How long, to the nearest tenth of a year, will it take the $10,000 to      Log On


   

Question 1148971: 1. Assume you invest $10,000 in a mutual fund (e.g. money market fund) at an APR of 7% compounded quarterly. How long, to the nearest tenth of a year, will it take the $10,000 to grow to $100,000? [Solve using both methods below.]

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


A+=+P%281%2Br%2Fn%29%5E%28nt%29

A = final value
P - beginning value (principal)
r = annual rate
n = number of compounding periods per year
t = number of years

100000+=+10000%281%2B.07%2F4%29%5E%28%284%2At%29%29

The unknown is in an exponent, so an algebraic solution requires logarithms. An easier method is using a graphing calculator. I will guess that those are the two solution methods "below"....

Using logs....

100000+=+10000%281%2B.07%2F4%29%5E%28%284%2At%29%29
10+=+%281.0175%29%5E%284%2At%29
log%28%2810%29%29+=+4t%2Alog%28%281.0175%29%29
t+=+%28log%28%2810%29%29%2Flog%28%281.0175%29%29%29%2F4

Use a calculator....

With a graphing calculator....

Y1 = 10000(1.0175)^(4x)
Y2 = 100000

Graph and find the point of intersection