Question

3. Suppose you borrow Pa dollars (called the principal) from a bank at 8 percent monthly interest and repay the amount in equal monthly payments of M dollars. (a) If P(t) is the money owed at time t, show that Plt + A1) - P(O)(1+3) - M: P(t) = P. (12) (b) Solve the above equation for P(1) (e) What should your monthly payments be to completely repay the loan in N years? (d) Suppowe you owe $50000 in student loans. The interest rate is $1.8% per vear. How much should you pay per month so that the loan is fully paid off in 10 years? (to determine monthly Interest, simply divide the annual interest by 12)

Answer 1

PI is the mene ouecl at time 6 2 O) Simple formula interest accorcin t interest on Plt Hne time perioel is (one mont in one one tme penid (P is the mently PLE p interest ate (net the peecentuye, percentese caividrd hy 100)) If Tetal amovot of ter ene P CI+P) we are also poyiny monty pament of m ot is one menth) is. Hime mone owe el aut ot PLtt Dt) botsou ed Po ar e begininz , money oued PCo) Po Usin Hne formula obtained in &), menej oweel in subsequent montas is: Po CP)m PLI P(2) Po CitP rM(i+p) - :P)-P (2) C1t A-rM = (6 CHA-M1+p) - M J Cit A) - m M (1+ p]° - MCHP) - (t+P)* : e) =

2. for k month money owecl m(re)k2 M C1 p - mCHP) - m (+A C PCK) senies The in the braete et s a gecmehnc senes irst term ith Co mmen Yutio p) and no of terms um s CtP) t the Hme mon ths in Plt oun in Nyeors loan Yepa the epoy the months money owed t=12N month cat shoulel be zero. 12n PC12N) Po CtB) -

MCP) 12 - Po P p2N :This shoutd be ne monthly Poyment Soo0o = interes trete is .&7.P.C mently interate yate is O.0o4 2100 10 years N = (1+ 0.004 12 (T0004)8 - oo4 M 525. 45 $ yeu shoul e 525.45 per menth in oreler poy so0o0 io pay o If your loan of

According to Chegg guidelines, I have answered Q3 with all four subparts. Please upload Q4 separately.