Question

(Solving for n with non-annual periods) Approximately how many years would it take for an investment to grow sixfold if it were invested at 13 percent compounded weekly? Assume that you invest $1 today. If you invest $1 at 13 percent compounded weekly, about how many years would it take for your investment to grow sixfold to $6? (Hint: Remember to convert your calculator solution to years.)

Answer 1

answer

final amount =principal (1+ (interest rate/no. of period interest applied))^{no. of times interest applied x no. of times periods elapse}

final amount (A)=$6

principal (P) =$1

interest rate (R) =13%=0.13

no. of period interst applied (N)=52

no. of times (t) = t

A= P(1+(R/N)^Nt

6=1(1+(0.13/52))^52t

6=(1+(0.13/52))^52t

6=(1+0.0025)^52t

6=1.0025^52t

using log on both sides

log_1.0025(6)=52t

log 6/log 1.0025=52t (log_ab=log b/log a)

0.79/0.0011 = 52t

718.2 = 52t

t=13.8 years

it will take 13.8 years to get the investment sixfold