Question

Marcel invests $2500 for 3 years at a rate of 1.6% per year simple interest. Jacques invests $2000 for 3 years at a rate of x% per year compound interest. At the end of the 3 years Marcel and Jacques receive the same amount of interest. Calculate the value of x correct to 3 significant figures.​

Answer 1

Using the information from marcel we can find the future value.
Fv= Pv(1+rt)
=2500(1+0.016*3)
=2620
Then we can fin CI
CI=Fv-PV
=2620-2500
=120
Since both have same amount of interest
Using Jacques information we can find future value
Fv=Pv+CI
=2000+120
=2120
Now we can find i(interest rate)
i=(FV/PV)^1/n -1
=(2120/2000)^1/3 -1
=(1.06)^1/3 -1
=1.0196-1
=0.0196
=1.96%
Therefore the internet rate for Jacques to get the same amount of interest is 1.96%.