Arithmetic reasoning

Question

Ellie wants to give her granddaughter a present of $500 saved in a bank account. If ellie puts $350 in the account which earns an 8% annual interest rate, how long must she wait before the account is worth $500

Answer 1

Hi Vivian.

 

Let's do this one year at a time:

 

After 1 year:  Start with $350  add the interest ($350)(.08) = $350 + $28 = $378  (not the $500 she wants)

After 2 years:  Start with $378 and add the interest ($378)(0.08) = 378 + $30.24 = $408.24   (not the $500 she wants)

After 3 years:  Start with $408.24 and add the interest ($408.24)(0.08) = $408.24 + $32.66 = $440.90   (not the $500 she wants)

After 4 years:  Start with $440.90 and add the interest ($440.90)(0.08) = $440.90 + 35.27 = $476.17   (not the $500 she wants)

After 5 years:  Start with $476.17 and add the interest ($476.17)(0.08) = $476.17 + $38.09 = $514.26  FINALLY!  she has reached more than $500.

 

I don't know what grade-level you are in, so in whole years, the answer is 5 years.

 

If you have worked with logarithms, you can discover that it is actually 4.63 years, or 4 years and 7 months and 17 days.