A financial planning service offers a college savings program. The plan calls fo

Question

A financial planning service offers a college savings program. The plan calls for you to make six annual payments of $15,000 each, with the first payment occurring today, your child’s 12th birthday. Beginning on your child’s 18th birthday, the plan will provide $27,000 per year for four years.

What return is this investment offering?

A financial planning service offers a college savings program. The plan calls for you to make six annual payments of $15,000 each, with the first payment occurring today, your child’s 12th birthday. Beginning on your child’s 18th birthday, the plan will provide $27,000 per year for four years.

Explanation / Answer

Here we need to calculate the interest rate that makes present value of annuity of $27,000, equal to future value of annuity of annual investment of $12,000. Or, PV of annuity = $27,000 * [{1 - (1+r)^-4} / r] Future value of annuity = $12,000 * {[(1+r)^6 - 1] / r} Equating the above two equation we have: 27,000 * [{1 - (1+r)^-4]} / r] = 12,000 * {[(1+r)^6 - 1] / r} or, 2.25 * [1 - (1+r)^-4] = [(1+r)^6 - 1] or, 2.25 - 2.25*(1+r)^-4 = (1+r)^6 - 1 or, 3.25 = 2.25(1+r)^-4+(1+r)^6 or, 3.25 = (2.25 + (1+r)^10 ) / (1+r)^4 or, (1+r)^10 - 3.25(1+r)^4 + 2.25 = 0 or, (1+r)^10 - 2.25(1+r)^4 - (1+r)^4 + 2.25 = 0 or, (1+r)^4 * [(1+r)^6 - 2.25] - 1*[(1+r)^6 - 2.25] = 0 or, [(1+r)^4 - 1]*[(1+r)^6 - 2.25] or, (1+r)^4 = 1, (1+r)^6 = 2.25 Solving the first equation, we get r = 0%, not feasible Solving the second equation, we get r = 14.4714% Investment is offering a return of 14.4714%

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