Question 1176681: The principal represents an amount of money deposited in a savings account subject to compound interest at the given rate.
Principal: $70,000
Rate: 6.0%
Compounded: daily
Time: 18 years
Find how much money there will be in the account after the given number of years.
A. The amount of money in the account after 18 years is ​$__.
​(Round to the nearest hundredth as​ needed.)
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! f = p * (1 + r) ^ n
f is the future value
p is the present value, also called the principal, in this type of problem.
r is the interest rate per time period
n is the number of time periods.
you are given that:
p = 70,000
r = 6% per year, compounded daily.
n = 18 years
6% per year compounded daily is equal to (6/365))% per day.
since the formula assumes rate, not percent, then:
(6/365)% per day = (6/365)% / 100 = 6/36500 per day. per day.
that would be equal to an interest rate of .0001643835616 per day.
18 years times 365 days per year = 18 * 365 = 6570 days.
the formula becomes:
f = 70000 * (1 + .0001643835616) ^ 6570 = 206,109.274.
round to the nearest hundredth and it becomes 206,109.27.
there is an online calculator that does the same for you.
this calculator works on percent, not rate.
your inputs to this calculator are:
pv = -70000
fv = 0
np = 18 * 365 = 6570
pmt = 0
ir = (6/365)% = .0164383562
payment at beginning or end doesn't matter, since pmt = 0.
click on fv and the calculator tells you that:
fv = 206,109.27
your entries are made without commas.
the calculator takes your interest rate as you gave it but rounds it to 6 decimal digits after it completes the calculation.
click on fv again, without changing any of the inputs, and you'll get a different answer because the calculator is now using the rounded input, rather than your original input.
it's a quirk of the calculator.
nothing to worry about as long as you know that your inputs have to be entered as you want them each time.
here's a display of the results of using this calculator.
first display is your inputs, as you entered hem.
second display is the output after you click on fv.
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