Suppose you have a habit of one $5 cup of Starbucks per week for 40 years,...

Suppose you have a habit of one $5 cup of Starbucks per week for 40 years, what is the reduction to the future value of your retirement account? What interest rate should you use?

Interest rate not given

Expert Solution

The interest rate you should use is the interest rate that you would earn on your retirement account.

As the interest rate is not given, we use the average retirement income fund category's return of 5.13%

If the cup of coffee is not bought, it could be invested to earn a 5.13% return. The future value (at the end of 40 years) of these weekly deposits is the reduction to the future value of your retirement account.

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

where P = periodic payment. This is $5.

r = periodic rate of interest. This is (5.13%/52). We divide by 52 since we need to convert the annual rate into weekly rate)

n = number of periods. This is 40 * 52 = 2080 (there are 40 years, or 2080 weeks in the period)

Future value of annuity = $5 * [(1 + (5.13%/52))²⁰⁸⁰ - 1] / (5.13%/52)

Future value of annuity = $34,340.19

Reduction to the future value of your retirement account = $34,340.19

jeff jeffy answered 2 years ago

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