Compound Interest Question

Question

You can afford monthly deposits of $140 into an account that pays 3.0% compounded monthly. How long will it be until you have $6,600 to buy a boat?

Type the number of months:___

(round to the next-higher month if not exact)

Answer 1

 6600 = 140 ( 1 + 0.03 ) ^n

 

  (1.03) ^n  = 6600/140 = 330/7 =

 

  n ( log 1.03) = log 330/7

 

   n = log ( 330/7) / log 1.03 =130. 36 months

  

 The way you mentioned is monthly interest rate is 3%, if it was compounded monthly with annual interest rate of 3% would be different, but the word annual is not mentioned here,

Answer 2

S = 140(1+0.03/12)^n + 140(1+0.03/12)^(n-1) + ... + 140(1+0.03/12)^1

 

140(1+0.03/12)S = 140(1+0.03/12)^(n+1) + 140(1+0.03/12)^n + 140(1+0.03/12)^(n-1) + ... + 140(1+0.03/12)^2

 

140(1+0.03/12)S - S = 140(1+0.03/12)^(n+1) - 140(1+0.03/12)^1

 

1 + S(140(1+0.03/12) - 1)/(140(1+0.03/12)) = 140(1+0.03/12)^n

 

n = ln(1 + 6600(140(1+0.03/12) - 1)/(140(1+0.03/12)) )/ln(140(1+0.03/12))