Sheldon just joined a new gym and signed up for a one-year membership. Membership fees can be paid in 12 monthly payments of $60, due at the beginning of each month or in one payment today. If the appropriate interest rate is 10%, how much should he pay today for the annual membership

Answer: $688.17

Explanation:

He has to pay $60 every month on the first day or a lump sum.

The lump sum will be the present value of monthly payments.

This is a stable Cashflow and so is an Annuity and because it is done on the first day of the month it is an Annuity due.

Calculating present value of annuity due is;

= Annuity + Annuity ((1 - (1 + r) ^ - (n - 1)) / r)

= 60 + 60 ((1 - (1 + 0.833%) - ¹¹) / 0.833%))

=60 + 60 * 10.4695

= $688.17

Note: interest rate must be divided into 12 to make it monthly rate.

=10%/12

= 0.833%