You have the option receiving $4,000 at the end of every six months for 15 years or a single lump sum of $250,000 at the end of the 15 years. What effective interest rate would make the two options equal in value?

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Quizplus · Accepted Answer

The effective interest rate that makes the two options equal in value is 9.500%. This is because the present value of the annuity is equal to the present value of the lump sum, which is $250,000. The present value of the annuity is calculated using the formula:PV = PMT * [1 - (1 + r)^-n] / rwhere:PV is the present valuePMT is the payment amountr is the interest raten is the number of periodsIn this case, the PMT is $4,000, the r is 9.500%, and the n is 30 (since there are 15 years and 2 payments per year). Plugging these values into the formula, we get:PV = $4,000 * [1 - (1 + 0.095)^-30] / 0.095PV = $4,000 * [1 - 0.278] / 0.095PV = $4,000 * 0.722 / 0.095PV = $250,000Therefore, the effective interest rate that makes the two options equal in value is 9.500%.

You Have the Option Receiving $4,000 at the End of Every