Question

Use the model A -Pent or A-P -->(1 +)" where A is the future value of P dollars 9 invested at interest rater compounded continuously or n times per year for 1 years. Victor puts aside $4,000 in an account with interest compounded continuously at 2.7%. How long will it take for him toearn $1000? Round to the nearest month. It will take approximately years and months for him to earn $1000.

Answer 1

SOLUTION;

P=$4000

I=$1000

A=$4000+$1000=$5000

r =2.7% = 0.027

Let's the t is time to take eran $1000

Now,

We know from questions to find the compound continuesly

$A=P.e^{rt}$

$5000=4000e^{0.027t}$

$e^{0.027t}=\frac{5}{4}$

$lne^{0.027t}=ln(\frac{5}{4})$

$0.027t=ln(\frac{5}{4})$

t = 8 years 3 month

The answer is = 8 years 3 month