You plan to buy a car in 12 years, one that you anticipate will cost $35,000. You have $10,500 to invest. If the interest is compounded monthly, what is the interest rate you need in order to get what you want?
Don't feel "I'm so bad at this question!" 90% of people do!.
Basically, what you are asking is this:
What interest rate will it take for $10,500 to grow to $35,000 in 12 years if it was compounded monthly? Well, your answer is=10.08%. But, how do we get that rate? Well, we use this foemula:
FV=PV [1 + R]^N, Where R=Interest rate per period, N=number of periods, PV=Present value, FV=Future value. So, we have:
35,000 =10,500[1 + R]^12*12 divide both sides by 10,500
3 1/3 =[1 + R]^144 take 1/144th root of both sides
1.00839597.. = 1 + R
R =1.00839597.. - 1
R=0.00839597 This is your interest rate month.
R=0.00839597 x 12 x 100
R=10.075% or 10.08% (rounded), your annual interest rate compounded monthly.
+37084 i = monthly interest rate (since it is compunded MONTHLY)
FV = Future Value PV = Present Value
FV = PV(1+i)^n Where n = number of interest periods(MONTHS)
35000 = 10500 (1 +i)^144
35000/10500 = (1+i)^144 Take LOG of both sides
.522878 = 144 log(1+i) Divide both sides by 144
.003631102 = log(1+i) Raise each side to the 10
10^(.003631102) = 1+ i
1.008395971 = 1 + i Subtract 1
.008395971 = i THAT is the MONTHLY rate YEARLY rate would be x 12 = .10075 or 10.075% Annual
