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Question 1085877: Deduce Compound rate of interest that will be required to produce $6,500 in 10yrs with initial deposit of $2,500.
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! FV = future value
PV = present value
r = interest rate
t = time in years
Note: I'm assuming the interest is compounded annually, so n = 1 which can be ignored in this case. For any other cases, then n would have to be included.
In this case,
FV = 6500
PV = 2500
r = unknown (we're solving for it)
t = 10
The formula we'll use is
FV = PV*(1+r)^t
Plug in the given values. Solve for r
FV = PV*(1+r)^t
6500 = 2500*(1+r)^10
6500/2500 = (1+r)^10
2.6 = (1+r)^10
(2.6)^(1/10) = ((1+r)^10)^(1/10) ... raise both sides to the power 1/10
1.10026509310602 = 1+r
1.10026509310602-1 = r
0.100265093106018 = r
r = 0.100265093106018
Rounding to four decimal places, we get
r = 0.1003
Which converts to r = 10.03% when we move the decimal point 2 spots to the right.
The interest rate is approximately 10.03%
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