Interest rate?

suppose you invest 5,000 dollars and would like your investment to grow to 10,000 in eight years. What interest rate, compounded weekley, would you have to earn in order for this to happen?





Please show how you did the problem|||You wish to multiply your money by 2 in 8 years or 416 weeks.


For annual compounding, the percentage interest rate per year is i where (1+i/100)^8 = 2, or i = 100*(2^(1/8)-1) = 9.050773%


For weekly compounding the percentage interest rate per week is j where (1+j/100)^416 = 2, or j = 100*(2^(1/416)-1). This is a very small percentage rate (0.166761%) because it is weekly. To compare it with the annual figure, multiply it by 52, giving 8.671562%.|||if the interest rate is i per week, then after week one you will have


5000(1+i)


week 2: 5000(1+i)(1+i)


week 3: 5000(1+i)^3


week 159: 5000(1+i)^159





and after 8 years (week 416)


5000(1+i)^416





So we want:


5000(1+i)^416 = 10,000


(1+i)^416 = 2


(1+i) = 2^(1/416)


1+i = 1.0016676


i = 0.0016676


Or 0.16676% per week





To work out the equivalent APR, compound this up 52 times:


1.0016676^52 = 1.090507


So to double your money in 8 years you need an APR of 9.05%





Note: 8 years isn't exactly 416= 8*52 weeks, so the actually weekly interest rate required would be slightly lower