This problem is confusing me. A straight-forward step by step answer would be ap

Question

This problem is confusing me. A straight-forward step by step answer would be appreciated. I need all parts answered. This should use partial derivatives.

Suppose you make monthly deposits of P dollars into an account that earns interest at a monthly rate of p%. The balance in the account after t years is B(P,r,t) = P[(1+r)12t-1/r] r) dollars, where r = p/100 (for example, if the annual interest rate is 9%. then p=9/12=0.75 and r = 0.0075) (a) Let the time of investment be fixed at t = 18 years. With a target balance of $100.000, find the set of all points (P,r) that satisfy B = 100.000. This curve gives all deposits P and monthly interest rates r that result in a balance of $100.000 after 20 years. (b) Repeat part (A) with B = 60,000, B = 80,000, and B = 120,000, and draw the resulting level curves of the balance function. (Include the B = 100.000 curve on the graph of the level curves. There should be one graph.)

Explanation / Answer

a) B = 100000

t = 18 years

20 years is a typo mistake. Just forget about it.

P [(( 1+r ) ^216 -1)/r] = 100000

p = 100000/ [(( 1+r ) ^216 -1)/r]

p = 100000*t / [(( 1+r ) ^216 -1)]

b) for B = 60,000

Curve will change to

p = 60000*t / [(( 1+r ) ^216 -1)]

for B = 80,000

Curve will change to

p = 80000*t / [(( 1+r ) ^216 -1)]

for B = 120,000

Curve will change to

p = 120000*t / [(( 1+r ) ^216 -1)]

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