Question

There are two memberships: a standard membership with an annual payment of $75, and a lifetime membership with a one-time payment of $750.

Assuming an infinite analysis period, determine the range of MARR values for which the standard membership is preferred.

Can you use the P/A formula and trial and error to solve this problem?

for i at 11.11% (as found in another posted question) = > 75 ( P/A, 11.11%, 100) = 675 which is less than 750

for i at 10% = > 75( P/A, 10%, 100) = 749.9 which is approximately equal to 750

for i at 9% = > 75( P/A, 9%, 100) = 833 which is greater than 750

So a MARR of greater than 10% makes standard preferred.

Any high value for n can be used.

Is this correct? If not please advise.

Answer 1

The answer and the method used are correct. (A higher value of n would yield a more accurate answer)

However, for an infinite series the solution can be checked using infinite GP series sum:

P = 75/(1 + r) + 75/(1 + r)² + ....... = 75/r

P = 750 = 75/r

r = 10%

Therefore, a higher value of r would make the RHS < LHS and standard membership with annual payment would be more preferred.