Ronisha invests $5000 in an account that earns 2.3% annual simple interest. After 3 years, Ronisha invests the interest earned i
n a second account. This account earns 3.2% annual interest. Ronisha leaves the money in this account until she has earned $55.20 in interest. Ronisha does not deposit or withdraw any money from the accounts. How long does Ronisha invest money into the second account?
Very complicated problem, but thank goodness I have too much time and am a nerd.
Basically model 1st account as so. Fv=pv(1+I)^N Fv future value Pv present value I interest N number years So first equation is interest earned after 3 years Y=5000(1+0.023)^3 Y=5353 (rounded up) So we know that the interest earned is 5353-5000 which is 353.
Now Ronisha (clearly the name of a future investment genius) invests these 353$ in a new account. Now remember we’re not solving for FV we’re cause we’re given that: 55.2$ However this is the interest earned not the future value. So if interest earned is fv - pv and we know pv Fv - 353 = 55.2 Fv = 408.2$ So now we reuse the formula 408.2 = 353(1+0.032)^x Now just solve for x: First divide both sides by 353 1.156 = 1.032^x Remember the log rule that states x=b^y is same as y=logb(x) So using the same logic: X= log1.032(1.156) Use some kind of calculator for that where you can adjust log base. But you basically get: X= 4.602 So Ronisha has to basically invest 5 years or 4.6 years which is 4 years and 7 months.
Omg nevermind, wait it’s simple interest…. Sorry here’s the simple solution. My bad, but I worked so hard on the top part I don’t want to delete it. I=prt Interest = principal * rate * time I= 5000(0.023)(3)=345 Then just do the same but plug 55.2 for I 55.2 = 345(0.032)t Now solve for t 55.2 = 11.04t t= 5
As you can see, similar logic where ultimately it takes 5 years. But this “genius” Ronisha should’ve just done compounding interest (my first calculation) and gotten it done in 4.6 years. Almost 5 months faster.
