Question 1161158: 1) Find the future value of a simple interest loan of $4,000 at 5.5% interest for 7 months?
2) Find the present value of $26,500 in 9 months at 5.8% interest.
3) Find the time required for an investment of 5000 dollars to grow to 6400 dollars at an interest rate of 7.5 percent per year, compounded quarterly.
Found 2 solutions by Theo, MathTherapy:
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! 1) Find the future value of a simple interest loan of $4,000 at 5.5% interest for 7 months?
simple interest rate formula is f = p*(1+r*n)
f = future value
p = present value
r = interest rate per time period
n = number of time periods
p = 4000
r = .055 per year
n = 7/12 years
f = 4000 * (1+.055*7/12) = 4018.3333333....
that's your future value.
2) Find the present value of $26,500 in 9 months at 5.8% interest.
simple interest rate formula is f = p*(1+r*n)
f = future value
p = present value
r = interest rate per time period
n = number of time periods
f=26500
r=.058 per year
n=9/12 years
26500 = p*(1+058*9/12)
divide both sides of this formula by (1+058*9/12) to get:
26500/(1+1.058*9/12) = 25395.30426
that's your present value.
3) Find the time required for an investment of 5000 dollars to grow to 6400 dollars at an interest rate of 7.5 percent per year, compounded quarterly.
compound interest formula is f = p*(1+r)^n
f = future value
p = present value
r = interest rate per time period
n = number of time periods
f = 6400
p = 5000
r = .075 per year divided by 4 = .07/12 per quarter.
n = number of quarters
formula becomes:
6400 = 5000*(1+.075/4)^n
divide both sides of the formula by 5000 to get:
6400/5000 = (1+.075/4)^n
take the log of both sides of this equation to get:
log(6400/5000) = log((1+.075/4)^n)
by properties of logs, this becomes:
log(6400/5000) = n*log(1+.075/4)
solve for n to get:
n = log(6400/5000)/log(1+.075/4) = 13.28891872
confirm by replacing n in original equation to get:
f=5000*(1+.075/4)^13.28891872 = 6400.
this confirms the solution is correct.
Answer by MathTherapy(10552)  (Show Source):
You can put this solution on YOUR website! 1) Find the future value of a simple interest loan of $4,000 at 5.5% interest for 7 months?
2) Find the present value of $26,500 in 9 months at 5.8% interest.
3) Find the time required for an investment of 5000 dollars to grow to 6400 dollars at an interest rate of 7.5 percent per year, compounded quarterly.
Answer for 1) from the other person is WRONG. Does he really think that investing $4,000 for 7 months could YIELD only $18 in interest?
$18 in interest represents an interest rate of .77%, which is less than 1%.
Correct answer:  , with Future Value being A
In terms of years (the usual time frame), 3) should be:  , with A being future value and t being time, in years.
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