Question 1116528: Rebecca put $35,000 in an education account on the day her daughter was born. If the account earned 7.75% interest compounded monthly, what was the total in the account when her daughter turned 18? Round the final answer to the nearest cent?
I can never set up an equation from a word problem please help me work through this.
Answer by addingup(3677)   (Show Source):
You can put this solution on YOUR website! 35,000(1+(0.0775/12)^12*18
35,000(1.00646)^216
35,000*4.02 = 140,700
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how is the formula derived?
Interest per period (per month): 0.0775/12 = 0.00646
month 1: 35,000 + (35,000 * 0.00646)
we can rearrange this equation like this:
35,000 * 1 + 35,000 * 0.00646
simplify:
35,000 * (1 + 0.00646)
simplify again:
35,000 * 1.00646
so, adding 0.00646 interest is the same as multiplying times 1.00646
To project this over time, instead of solving month 1, taking the new total and then solving month 2, etc. it's easier to do it using exponents, like this:
Period: monthly compounding over 18 years = 12*18 = 216
35,000 * 1.00646^216
:
Happy learning,
John
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