Require that X*(1.025)^16 = 15,000.
X is the initial amount that you will need to invest.
The 1.025 is the factor by which balance increases by every 3 months. It does this 16 times in 4 years.
You can use logs to get the answer. I will use base 10 logs. (The base does not matter, as long as you are consistent and use the same log base on both sides of the equation)
log 15000/X = 16 log 1.025 = 0.1715818
15,000/X = 1.4845056
X = $10,104.37
Barbara knows that she will need to buy a new car in 4 years. The car will cost $15,000 by then. How much should she invest now at 10%, compounded quarterly, so that she will have enough to buy a new car? Round to the nearest cent.
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