Question

Sigmund is now 25 and working. He plans to take a year off when he is 35 and to travel during that year. To allow him to take the year off he needs to save $23,488 by making monthly deposits in a savings account every month over the ten years from his 25th birthday to his 35th birthday. Assume that the savings account will pay an interest rate of 4% over those ten years and assume that there is no money in the savings account on Sigmund’s 25th birthday.

1. What is the interest rate per payment period (r)?

2. What is the total number of payments (n) into the account during the 10 years that Sigmund is saving for his year off?

3. What amount must Sigmund deposit into the savings account each month during the ten years?

Answer 1

1]

r = interest rate per period = annual rate /12 = (4%/12)  

2]

n =  total number of payments = number of years * 12 = 10 * 12 = 120

3]

Future value of annuity = P * [(1 + r)ⁿ - 1] / r,

where P = periodic payment. We need to calculate this.

r = periodic rate of interest. This is (4%/12).  

n = number of periods. This is 120

$23,488 = P * [(1 + (4%/12))¹²⁰ - 1] / (4%/12)

P = $23,488 * (4%/12) / [(1 + (4%/12))¹²⁰ - 1]

P = $159.51

Sigmund must deposit $159.51 into the savings account each month