Question

Jarad, a middle school student, receives $5000 from his grandmother. He decides to invest it in an interest-bearing account, in hopes of earning enough interest to buy a car at a later date. Jarad deposits the entire amount into an account that pays 6.3% interest, compounded weekly. How many weeks must Jarad wait for the investment to reach a value of $6700? Round your answer up to the next complete week and assume that there are exactly 52 weeks in a year. Number of weeks Number of weeks

Answer 1

242 weeks

Step-by-step explanation:

After n weeks at annual interest rate r, the principal amount P will result in account balance A according to ...

... A = P·(1 +r/52)^n

Taking logs, we get

... log(A) = log(P) +n·log(1 +r/52)

... (log(A) -log(P))/log(1 +r/52) = n . . . . . solve for n

Filling in the given informatin, we have ...

... (log(6700) -log(5000))/log(1 +.063/52) = n ≈ 241.71

Rounded to the next higher number of weeks, this is 242 weeks.