Business math Word problem

Question

A loan of $40,000 at 6% is due in 16 months. Find the present value of the loan if the time value of money is 10%. 

Answer 1

A=P(1+r/n)^nt where

P=Present value

A= Amount due = $40,000

in t years = 16/12 = 4/3 yrs

compounded n times per year

at r=6% APR, Annual Percentage = .06

if n=1

40000= P(1.06)^(4/3)

solve for P

P= 40,000/(1.06)^(4/3) = $37,009.98 rounded to nearest cent

if compounding is continuous and n=infinity

then

A=Pe^rt

40000=Pe^.06(4/3)= Pe^.08

P =40,000/e^.08 = $36,924.65

compounding daily is slightly larger than for contintuous

compounding quarterly or monthly are somewhere between continuous and annual compounding

all about $37,000