Calculus Solving for Present value of payments

[alexs2jennisha]

Homework Statement

You value a car to be $30,000. If you plan to make continuous payments over 5 years and at an interest rate of r = :1.

1) How much should you pay per year so that the present value of your total payments in 30; 000?
2)What if instead you decided to let your payments increase with time and pay at a rate of $6000 + t1000 per year, where t is measured in years. How long would it take you to pay o the car ? (Note the equation you get might be dicult to solve, so you can use a graphing calculator to estimate.)

Homework Equations

The formula that i think i should use is

PV = PMT(1-(1/(1+i)^n)) / i

The Attempt at a Solution

For part 1:

solving for PMT I got 7913.48. Did i do that correctly?


For part 2:
Im not too sure how to approach this. Do i use the same equation and solve for t? I assume the t is the same as the n i used in my pv formula, is this correct?

Thanks

 

[SteamKing]

What does r = :1. mean? What does making 'continuous payments' mean?

 

[Ray Vickson]

Homework Statement

You value a car to be $30,000. If you plan to make continuous payments over 5 years and at an interest rate of r = :1.

1) How much should you pay per year so that the present value of your total payments in 30; 000?
2)What if instead you decided to let your payments increase with time and pay at a rate of $6000 + t1000 per year, where t is measured in years. How long would it take you to pay o the car ? (Note the equation you get might be dicult to solve, so you can use a graphing calculator to estimate.)

Homework Equations

The formula that i think i should use is

PV = PMT(1-(1/(1+i)^n)) / i

The Attempt at a Solution

For part 1:

solving for PMT I got 7913.48. Did i do that correctly?


For part 2:
Im not too sure how to approach this. Do i use the same equation and solve for t? I assume the t is the same as the n i used in my pv formula, is this correct?

Thanks

What does r = :1 mean? Do you mean to write r = 0.1? Is that the *annual* rate (that is, the interest rate is 10% per year)?

Your formula is for discrete payments at regularly-spaced points in time, but the problem asked for a *continuous* stream of payments, and presumably using *continuous* compounding/discounting. That will turn an arithmetic/algebraic problem into a calculus problem! So, you need the formulas for continuous-time discounting.

 

[bagram]

I'm pretty for q1 you need to use a continuous paying annuity formula which is $PV=PMT*((1-v^n )/delta)$ where $delta=ln(1+r)$ and $v=1/(1+r)$

 

[Ray Vickson]

I'm pretty for q1 you need to use a continuous paying annuity formula which is $PV=PMT*((1-v^n )/delta)$ where $delta=ln(1+r)$ and $v=1/(1+r)$

I am 100% sure you should not use this formula.