Kevin Zhou — Mechanics Review Problem 2 · Kevin Zhou #MRev.2
Physics · mechanics
Problem
Problem 1. At some point in your life, you might have to buy a very expensive item of price P
financed by a loan. If the loan has a monthly interest rate r ≪ 1 (e.g. r = 1% means your debt
grows by 1% per month), then it turns out you can pay it all off in N months if you pay
r(1+r)N
C = P
(1+r)N −1
per month. For example, if r = 0 then C = P/N.
(a) Find an approximation for C valid for small rN.
(b) Find an approximation for C valid for large rN.
2 Statics and Linear Dynamics