A student wants to save $8000 for college in five years. How much should be put every year into an account that earns 5.2 percent annual interest?
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The student wants to have $8000 at the end of 5 years by placing a certain amount in an account every year where he is able to earn 5.2 interest annually.
Let the amount be X. The amount that is placed in year 1 increases to X*(1 + 5.2%)^5 after 5 years and the amount placed in year 2 increases to X*(1 + 5.2%)^4. In the same way we can derive what the amount placed in the other years becomes.
At the end of year 5 he has $8000
X * [ (1.052)^5 +(1.052)^4 +(1.052)^3 +(1.052)^2 +(1.052)^1] = 8000
The series within the brackets is a GP, with the first term 1.052 and the common ratio 1.052. The sum of 5 such terms is 1.052*( 1.052^5 – 1) / ( 1.052 – 1)
=>1.052*( 1.052^5 – 1) / ( 0.052)
=> 5.836
X = 8000 / 5.836
=> $1370.8
The student should put $1370.80 into the account every year.
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