Homework Answers
Two-year subscription and two successive one-year subscriptions are equivalent when:
Present Value of two-year subscription = Present Value of first-year subscription + Present Value of second-year subscription
(NOTE: Present Value of two-year subscription and the present value of the first-year subscription of two successive one-year subscriptions are $28 and $15 respectively, i.e, the same as the given cost because it is paid at the beginning which is the present period hence the cost itself is the present value)
$28 = $15 + Present Value of second-year subscription
Present Value of second-year subscription = $28 - $15 = $13
Present Value of second-year subscription + (Present Value of second-year subscription * Interest Rate) = Future Value (renewal cost) of the second year subscription
$13 + ($13 * Interest Rate) = $16.50
$13 * Interest Rate = $16.50 - $13 = $3.50
Interest Rate = $3.50/$13 = 0.269 or 27% approx
Hence the annual effective interest rate that makes the two-year subscription equivalent to two successive one-year subscriptions in 27% approximately.
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