Question

A high school student is working to save for college. She has a job with the town as an intern that pays her $120 weekly. Miraculously, she has found a savings account that pays interest at 2% compounded monthly. She plans to put all of her earnings into this account for the next two years and hopes to be able to pay for her first year of tuition with her savings – which will cost $15,000. • Will she accomplish her goal? Show your calculations.

Answer 1

We can convert the entire timeline into yearly payments to avoid any errors in calculation. We have 52.14 weeks in a year so we can say that per year we are getting (52.14*120) in total for 2 years. Now the monthly compunded rate is 2%. We convert this to yearly rate using the relation -

Now she need $15000 at the end of two years. If we are taking weekly payments, we can consider the payments to be made continuously over the two years period which is a very close approximation. Now using annuities we can get the accumulated value (AV) as shown below -

Thus she will have ample amount to fund her college tuition fee with the fee.

THANK YOU.