Question

Mike just joined a new gym and signed up for a one-year membership. Membership fees can be paid in 12 monthly payments of $55, 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 1

Above is case of annuity due.

Monthly amount (PMT) = $55

Monthly Interest rate (i) = 10% / 12 = 0.8333%

No of monthly payment (N) = 12

Therefore Present value of monthly annuities to be paid at the beginning of each month (PV) =

= PMT x [1 - 1/(1+i)ⁿ] x (1+i)/i

Therefore, PV = 55 x [1 - 1/(1+0.008333)¹²] x (1+0.008333)/0.008333

Therefore, PV = $630.81

Therefore, Amount Mike should pay today for the annual membership = $630.81

Alternatively, above can be done using financial calculator or PV function in excel.

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Comment if further doubts in above.