Li B. answered • 09/30/15

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Experienced HS Teacher with Expertise in Math and Science

Define terms:

A = amount = $2000

P = principle (amount put down in the beginning) = $800

r = interest rate (per year) = 4% = 0.04

t = number of years (what we are solving for)

Equation to calculate:

A = P (1 + r/n)

^{nt}n is the number of time the interest is compounded per year (in this case, n=1 since the interest is compounded annually)

So we have a simplified equation:

A = P (1 + r)

^{t}Plug in numbers:

2000 = 800(1.04)

^{t}2.5 = 1.04

^{t}Take natural log of both sides

ln 2.5 = t * ln 1.04

0.916 = t * 0.0392

t = 23.367 = 24 years (we round up since it will take more than 23 years to reach 2000)