Question

Briana invested $12,500 into a fund that is expected to grow by 5.25% per year.

How long with it take the fund to be worth $25,000? Round to the nearest year.
A) 2 years
B) 12 years
C) 14 years
D) 10 years

Answer 1

It would take: C. 14 years.Good luck!

Answer 2

Option C - 14 years

Explanation:

Given : Amount invested = $12,500 , growth rate = 5.25% , Amount fund = $25,000

Using formula :
`A=P(1+r)^t`

Where,

P = principal amount = 12,500

r = annual rate of interest = 5.25%= 5.25/100=0.0525

t = number of years the amount is deposited or borrowed for, in this case we don't know it

A = amount of money accumulated = $25,000

Putting values in the formula we get,

`A=P(1+r)^t`

`25000=12500(1+0.0525)^t`

`(25000)/(12500)=(1+0.0525)^t`

`2=(1.0525)^t`

Taking log both side,

`log2=log(1.0525)^t`

By property of logarithm
`logx^a=alogx`

`log2=tlog(1.0525)`

`(log2)/(log1.0525)=t`

`t=(0.301)/(0.022)`

`t=13.68`

Approx t=14 years

Therefore, Option C is correct.