Question

amount $50,000.00; interest rate 17%; comp. annually; due in 12 years. What is the amount must be payed immediately?

Answer 1

To find the present value of the $50,000, you need to discount it (using the interest rate) back 12 years.
The equation to do so will look like this:

Present Value * (1+r)^t = Future Value

Where:
Present Value = What we’re trying to find (I’ll call it X)
r = the interest rate (17%)
t = time, in years (12 years until maturity)
Future Value = The amount paid out in 12 years time ($50,000)

Plug these values in and we get:

X * (1+0.17)^12 = 50,000
\[X = 50000\div(1.17)^{12}\]
X = $7,598.71 (rounded)

Answer 2

here is another solution. is a bit more complicated and not so accurate, but more flexible. it is based on the formula named "double time"
ln(growth factor)*100/time=growth rate

ln(50000/x)*100/12=17
ln(50000/x)*100=204
ln(50000)/ln(x)*100=204
(10.8-ln(x))*100=204
1008-100lnx=204
-100ln(x)=-898
lnx=8,98
x=7942

the accuracy of the solution depends strongly on the accuracy of calculation of ln(50000) and e^8,98

Answer 3

Thanks you guys