Solution for Problem 8.3.4

Find the value of $20,000 left on deposit for 30 years
at an annual rate of 9% compounded monthly.

This is a geometric sequence problem.
 
an = a0(1+ r)Let a0 = initial value.

Solve Step

a0 = 20,000

a0 = initial value
r = 0.09 ÷ 12 = 0.0075 =  9% annual rate divided by 12 (monthly is 12 times a year)
n = 30 × 12 = 360 n = number of years times by 12 (monthly is 12 times a year)

a360 = 20,000(1 + 0.0075)360 

a360 = 20,000(1.0075)360 » $294,611.52

The account would have $294,611.52 at the end of 30 years.