Question

Rick 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 8%, How much should he pay today for the annual membership?

Answer 1

Monthly installment = 55

Interest rate = 8% per annum

Monthly interest rate = 8/12 = 0.66%

time period = 12 months

By the help of present value of annuity due = R*[1-(1+i)^(-n)]/(i)*(1+i)

where R - periodic payment

n - no. of compounding periods

i - Interest rate per compouding period

= 55*[1-(1+0.08/12)^(-12)]/(0.08/12)*(1+0.08/12)

= 55*[(1-0.923361]/(0.08/12)*(1+0.08/12)

= 55*[0.076639]/(0.00667)*1.00667

= 55*11.496*1.00667

= 636.48

so he should pay today 636.50 for annual membership.

Please comment in case of further clarification.