corbyn2316
contestada

You invest $6500 into a mutual fund that is expected to earn 6% per year. How long will it take the fund to be worth $13,000?

Respuesta :

MrBrainalot
This is a compound interest problem so you cannot use the simple interest formula. Effectively the total amount is being compounded each year by 6%. There is a formula for compound interest but in this simple example you can work this out recursively.

year 1 = 6500
year2 = 6500*1.06 = 6890
year3 = 6890*1.06 = 7303
year4 = 7303*1.06 = 7741..
etc......
year12 = 11604*1.06 = 12338 

abidemiokin

It will take about 12 years to worth 12 years to worth $13,000

Compound interest

The formula for calculating compound interest is expressed as:

[tex]A = P(1+r)^t[/tex]

Given the following parameters:

  • A = $13,000
  • P = $6500
  • r = 6% = 0.06

Substitute into the formula

[tex]A = P(1+r)^t\\ 13000 = 6500 (1+0.06)^t\\ 2 =(1.06)^t\\ ln2=tln1.06\\ 0.6931 =0.0583t\\ t=\frac{0.6931}{0.0583}\\ t \approx 12 years[/tex]

Hence it will take about 12 years to worth 12 years to worth $13,000

Learn more on compound interest here; https://brainly.com/question/24924853

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