In an episode of the Andy Griffith Show, Mayberry resident Frank Myers almost lost his home to taxes owed. Luckily, Sheriff Andy Taylor found an old town bond that belonged to Frank. The bond's original value was $100 paying 8.5% interest compounded annually and was 100 years old. Determine the amount the town of Mayberry now owed Frank on this bond.
what is
100(1.085)^100 ??
This episode annoys me a bit because that would be the amount if it was exactly 100 years old even though the episode clearly says it is over $100 years old. another annoying thing is that even though the show was shot in the 60s, the setting takes place in the 30s as stated by Andy Griffith in an interview. If you watch, the bond is from 1861 and if it was 100 years old then it would be 1961 not in the 1930s. so yeah, that was me over analysing a show from the 60s on an obscure website that no one will ever see
$349,119.27
One would know the show is obviously set in the 60s by looking at Sheriff Andy’s patrol car.
To determine the amount the town of Mayberry owed Frank on the bond, we need to calculate the compounded value of the bond after 100 years.
The formula to calculate the future value (FV) of an investment with compound interest is:
FV = PV * (1 + r)^n
Where:
FV is the future value
PV is the present value (original value of the bond)
r is the interest rate (in decimal form)
n is the number of periods (or years in this case)
In this case, the present value (PV) of the bond is $100, the interest rate (r) is 8.5% or 0.085 (in decimal form), and the number of periods (n) is 100 years.
Let's calculate the future value:
FV = $100 * (1 + 0.085)^100
To calculate this, you can use a calculator or a spreadsheet software like Microsoft Excel or Google Sheets.
The future value of the bond would be the amount the town of Mayberry owes Frank after 100 years.