How much money should be invested in an account that earns 8% annual interest compounded monthly in order to have $4,000 in 5 years?
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calendarEducator since 2011
write51 answers
starTop subjects are Math and Literature
We are asked to find the amount of money which must be invested to have $4000 in an account at the end of five years if the annual interest rate is 8% compounded monthly.
We will use the following formula:
=>A(t) = P( 1 + r/n) ^nt
P = principal
A = the amount after t years
r = the investment rate
n= number of times interest compounds per year
t = number of years
=> A(t) = P( 1 + r/n) ^nt
=> 4000 = P ( 1 + .08/12)^12(5)
=> 4000 = 1.4898P
=> 2684.92 = P
The amount to invest is 2684.92.
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calendarEducator since 2010
write12,551 answers
starTop subjects are Math, Science, and Business
The interest rate earned in the account is an annual rate of 8% compounded monthly.
So the monthly rate of interest is 8/12 = 2/3 %. Let the amount to be invested initially be P. In 5 years or 5*12 = 60 months this has to become $4000.
P*(1 + (2/3)%)^60 = 4000
=> P( 1+2/300)^60 = 4000
=> P(302/300)^60 = 4000
It is easier to use log here to determine P
log [ P(302/300)^60] = log 4000
=> log P + 60*log (302/300) = log 4000
=> log P = log 4000 - 60*log (302/300)
=> log P = 3.428
P = 10^3.428
=> P = 2684.84
The initial amount to be deposited is $2684.84