Question 1199059: Hello, I am having trouble with using a TVM solver. I am not sure if I'm getting the right answers. I'd love it if someone could help me. The question is:
Use a TVM Solver:
A) $2,500.00 investment earns interest at 7.5% compounded monthly. How long will it take it to double?
B) At what interest rate should $1,500.00 be invested, if you want to have $2,000.00 in 10 years compounded daily?
Answer by math_tutor2020(3817)   (Show Source):
You can put this solution on YOUR website!
If you have a TI83 or TI84, then follow the steps mentioned below.
If not, then skip to the next section.
Press the button labeled "APPS".
It is likely a different color from the rest of the buttons.
Go to "Finance", then "TVM Solver"
Check out this page for a few examples
https://people.tamu.edu/~kahlig//calc/tvm-solver.html
For part (a), type the following values
N = 0
I = 7.5
PV = -2500
PMT = 0
FV = 5000
P/Y = 1
C/Y = 12
N = number of periods = number of years in this case
I = interest rate in percent form
PV = present value
PMT = payment per period
FV = future value
P/Y = the number of payments per year
C/Y = the number of compounding periods per year
The PV is negative because it's a cash outflow.
Positive values are cash inflows.
The PMT is 0 because you aren't making periodic deposits; rather you make a one-time deposit.
After those values are inputted, scroll back up to the first line N = 0
Then press the green "alpha" key and then hit "enter"
This will then solve for N to get roughly 9.270813549
In other words, the N = 0 will update to N = 9.270813549
It takes about 9.270813549 years for the money to double at this interest rate, when compounded monthly.
0.270813549 years = 12*0.270813549 = 3.249762588
telling us that
9.270813549 years = 9 years + 3.249762588 months
In short, it takes about 9 years + 4 months for the money to double.
I rounded up to the nearest whole month to guarantee the money cleared the doubling threshold.
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Here's an alternative TVM solver if you don't have a TI83 or TI84 calculator.
https://www.geogebra.org/m/mvv2nus2
The person who made this did so with the goal of emulating the TI83/TI84 calculator's TVM solver.
The inputs for that calculator would be the same as mentioned earlier.
Here's another alternative TVM solver
https://arachnoid.com/finance/
While this solver doesn't allow you to specify compounding frequency, we can make an adjustment on the interest rate.
Instead of 7.5%, we would have (7.5%)/12 = 0.625% as the monthly interest rate
That TVM solver will produce N = 111.25 to indicate 111.25 months
111.25 months = (111.25)/12 = 9.2708 years approximately
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Let's say we wanted to know what's going on under the hood of these TVM solvers.
Recall the compound interest formula is
A = P*(1+r/n)^(n*t)
where,
A = final value after t years
P = deposit
r = interest rate in decimal form
n = number of times the money is compounded per year
t = number of years
In the case of part (a)
A = 5000 which is double of 2500
P = 2500
r = 0.075
n = 12
t = unknown
So,
A = P*(1+r/n)^(n*t)
5000 = 2500*(1+0.075/12)^(12*t)
5000/2500 = (1.00625)^(12*t)
2 = (1.00625)^(12*t)
log( 2 ) = log( (1.00625)^(12*t) )
log( 2 ) = 12*t*Log( 1.00625 )
t = log(2)/(12*log(1.00625))
t = 9.270813549
We get the same answer as earlier to help confirm the answer is correct.
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Everything mentioned so far was for part (a)
Now onto part (b)
Go back to your favorite TVM solver of choice to plug in these values:
N = 10
I = 0
PV = -1500
PMT = 0
FV = 2000
P/Y = 1
C/Y = 365
The I = 0 will be updated after we use the solver to determine the interest rate.
For some TVM solvers, you'll leave that entry blank.
After using the TVM solver, you should get I = 2.88% approximately
Here's what the steps look like if we were to use the compound interest formula so we can solve for the variable r.
A = P*(1+r/n)^(n*t)
2000 = 1500*(1+r/365)^(365*10)
2000/1500 = (1+r/365)^(3650)
1.333333333 = (1+r/365)^(3650)
(1+r/365)^(3650) = 1.333333333
1+r/365 = (1.333333333)^(1/3650)
1+r/365 = 1.00007882
r/365 = 1.00007882 - 1
r/365 = 0.00007882
r = 365*0.00007882
r = 0.0287693
We get an interest rate of roughly r*100% = 0.0287693*100% = 2.87693% which rounds to 2.88% found earlier.
This helps confirm the answer.
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Summary:
Answer to part (a) is 9.27 years, or 9 years, 4 months when rounding up to the nearest month.
Answer to part (b) is 2.88%
Each answer is approximate.
Round each decimal value according to the instructions your teacher provides; or seek further clarification of rounding instructions.
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