US Savings Bonds

Question: Population growth q: A US savings bond for $500 as an interest reate of 11% compounded monthly…?

A US savings bond for $500 as an interest reate of 11% compounded monthly…?
a. How much will the bond be worth when it matures after 25 years?

b. if the annual rate of inflation (which lowers the value of money) is 3% during those 25 years, the value of the bond will be less. What will its value be after 25 years?

Explain why.

Answer: a) since interest is compounded monthly adjust the interest rate to per month
r = 11/12% per month, n = 12×25 months
using compound interest formula

Value at end of 25th year = 500(1 + (11/12)/100)^(12×25)

b)
value at end of each year = compounded value – inflation
value end of 1st year
= 500(1 + (11/12)/100)^12 – 0.3(500( 1 + (11/12)/100)^(12)) = 0.7(500(1 + (11/12)/100)^12)

value end of 2nd year = value end of 1st year – inflation
= 0.7(500(1 + (11/12)/100)^12) – 0.3×0.7(500(1 + (11/12)/100)^12)
= 0.7^2(500(1 + (11/12)/100)^12)

value end of 3rd year = value end of 2nd year – inflation
= 0.7^2(500(1 + (11/12)/100)^12) – 0.3×0.7^2(500(1 + (11/12)/100)^12)
= 0.7^3(500(1 + (11/12)/100)^12)

looks like a pattern is developing!

Value end of 25th year = 0.7^25(500(1 + (11/12)/100)^12

You need to calculate these as ALL the hard work has been done for you!

Rare Recording of Ludwig von Mises: Wage Earners and Employers