Problem 5: At a certain rate of compound interest, 1 will increase to 2 in a yea
ID: 2692478 • Letter: P
Question
Problem 5: At a certain rate of compound interest, 1 will increase to 2 in a years, 2 will increase to 3 in b years, and 3 will increase to 15 in c years. If 6 will increase to 10 in n years, express n as a function of a, b, and c .Explanation / Answer
One solution method is the following: 2=(1+r)^a ==> a=log(2) 3=2(1+r)^b ==> b=log(3/2) 15=3(1+r)^c ==> c=log(5) 10=6(1+r)^n ==> n=log(10/6) where the logs are taken in base (1+r). Then, n=log(10/6) =log(10)-log(6) =[(log(5)+log(2)]-[log(3/2)+2log(2)] = [c+a]-[b+2a] = c-a-b By the way, (1+i)^(a+b+c) = 15 does not imply i = 15^-(a+b+c) - 1.