SOLUTION: How much money should be deposited today in an account that earns 6.5 % compounded monthly so that it will accumulate to $ 14,000 in three​ years? I got 2,478.29

Algebra ->  Customizable Word Problem Solvers  -> Finance -> SOLUTION: How much money should be deposited today in an account that earns 6.5 % compounded monthly so that it will accumulate to $ 14,000 in three​ years? I got 2,478.29       Log On

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Question 1072699: How much money should be deposited today in an account that earns 6.5 %

compounded monthly so that it will accumulate to $ 14,000

in three​ years?
I got 2,478.29 and it is wrong. All i have done is plug it into my calculator.
Found 3 solutions by Fombitz, Theo, rothauserc:
Answer by Fombitz(32388) About Me  (Show Source):
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
your annual interest rate is 6.5% / 100 = .065

there are 12 months in the year.

your number of months is equal to 12 * 3 = 36

your monthly rate is .065 / 12 = .005416666.....

the formula is f = p * (1 + r) ^ n

f is the future value
p is the present valued
r is the interest rate per time period.
n is the number of time periods.

your time periods are in months.

replace f with 14000 and replace r with .005416666.... and replace n with 36 and your formula becomes:

14000 = p * (1.005416666....) ^ 36

divide both sides of this equation by (1.005416666....) ^ 36 to get:

14000 / ((1.005416666....) ^ 36) = p

solve for p to get:

p = 11525.74876

Answer by rothauserc(4718) About Me  (Show Source):
You can put this solution on YOUR website!
The compound interest formula is
:
Amount(A) = Principal(P) * (1 + rate(r)/number of times interest is compounded per year(n))^(n*time(t))
:
using variables
:
A = P * (1 + r/n)^nt
:
n = 12, t = 3, r = 0.065, A = 14000
:
14000 = P * (1 + 0.065/12)^36
:
P = 14000 / (1 + 0.065/12)^36 = 14000 / 1.2147 = 11525.48
:
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The amount to be deposited today is $11525.48
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