Could someone tell me the rate for a $6000
gift that grew to 7,000,000 over 200 years?
7.000,000=6000*(1+p)^200
log(7.000,000)=log(6000)+log[(1+p)^200)]
log(7.000,000)=log(6000)+200*log(1+p)
log(7.000,000)-log(6000)=200*log(1+p)
Divide both sides with 200
[log(7.000,000)-log(6000)]/200=log(1+p)
log(1+p)=[log(7.000,000)-log(6000)]/200
log(1+p)=(6.8450980400142568307122162585926-3.7781512503836436325087667979796)/200
log(1+p)=3.066946789630613198203449460613/200
log(1+p)=0.015334733948153065991017247303065
1+p=10^0.015334733948153065991017247303065
1+p=1.0359403135706036366295577484724
p=1.0359403135706036366295577484724-1
p=o.0359403135706036366295577484724
p=1.0359403135706036366295577484724*100%
p=3.5940313570603636629557748472399%
Correction:
p=0.0359403135706036366295577484724*100%
p=3.5940313570603636629557748472399%
To find the rate for a gift that grew from $6000 to $7,000,000 over a period of 200 years, we can use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A = the final amount ($7,000,000)
P = the initial principal ($6000)
r = annual interest rate (which we need to find)
n = number of times interest is compounded per year (assuming it's compounded annually)
t = number of years (200 years in this case)
Since we are trying to find the rate (r), we can rearrange the formula to solve for it. Divide both sides of the equation by P, take the nth root of both sides, and then subtract 1:
(7,000,000 / 6000)^(1 / (200 * 1)) - 1
Simplifying this expression will give us the rate.
Calculating the expression, we find the rate to be approximately 0.0774 or 7.74%.
Therefore, the gift grew at an average annual rate of 7.74% over 200 years.