Question 891878: How much should be deposited in an account paying 4.75% interest, compounded semi-annually, in order to have a balance of $7,000 after 5 years and 6
months?
Enter the answer in dollars and cents, and round to the nearest cent, if needed. Do not include the dollar sign. For example, if the answer is $0.61, only the
number 0.61 should be entered.
Principal $ ____________
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! We'll use the formula A = P*(1+r/n)^(n*t) where...
A = 7000
P = unknown
r = 4.75% = 0.0475
n = 2 (compounding 2 times per year)
t = 5 yrs, 6 months = 5.5 years
Plug those values in and solve for P to get
A = P*(1+r/n)^(n*t)
7000 = P*(1+0.0475/2)^(2*5.5)
7000 = P*(1+0.02375)^(11)
7000 = P*(1.02375)^(11)
7000 = P*1.29459242778672
7000/1.29459242778672 = P
5407.1071711484 = P
P = 5407.1071711484
P = 5407.11
You need to deposit $5,407.11
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