Nicole was born 18 years ago. On the day Nicole was born, her dad decided that s

Question

Nicole was born 18 years ago. On the day Nicole was born, her dad decided that she should go to college when she becomes 18 years old and therefore he decided to save money for her to be able to go to college. On the day Jane was born, her dad put $12,000 in a saving account that earns 6% interest compounded quarterly. Five years ago, Nicole's mom noticed that the account would not reach the amount needed for college. So, 5 years ago, she put in the account $600 every month at an interest rate earning 4% compounded monthly.
1- Find the total amount needed for Nicole to go to college.
2- Find the total amount Nicole's Mom and Dad put in the account.
3- Find the total amount of interest the account earned.

Explanation / Answer

Amount Needed=12000*(1+6%/4)^(4*18)+600*(1+4%/12)^59+600*(1+4%/12)^58.........600*(1+4%/12)+600

=12000*(1+6%/4)^(4*18)+600*(1-(1+4%/12)^60)/(1-(1+4%/12))

=$74833.28

Total Amount put=12000+600*60=$48000

So, Interest earned=74833.28-48000=$26833.28

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