Annuity Due Simple Problem - Logic Question

I got this problem wrong on my practice exam, and for some reason the logic just isn’t clicking right now. Why are we discounting the entire payments at 10% to today given discount rates are at 9% for the 1st 12 months? Can anyone do a better job explaining this than Kaplan’s answer pasted below? Maybe my brain is fried right now. Thank you.

Natalie Brunswick, neurosurgeon at a large U.S. university, was recently granted permission to take an 18-month sabbatical that will begin one year from today. During the sabbatical, Brunswick will need $2,500 at the beginning of each month for living expenses that month. Her financial planner estimates that she will earn an annual rate of 9% over the next year on any money she saves. The annual rate of return during her sabbatical term will likely increase to 10%. At the end of each month during the year before the sabbatical, Brunswick should save approximately:

A)

$3,505.00

Failed

B)

$3,330.00

Failed

C)

$3,356.00

Achieved

Explanation

This is a two-step problem. First, we need to calculate the present value of the amount she needs over her sabbatical. (This amount will be in the form of an annuity due since she requires the payment at the beginning of the month.) Then, we will use future value formulas to determine how much she needs to save each month (ordinary annuity).

Step 1: Calculate present value of amount required during the sabbatical

Using a financial calculator: Set to BEGIN Mode , then N = 12 × 1.5 = 18; I/Y = 10 / 12 = 0.8333; PMT = 2,500; FV = 0; CPT → PV = 41,974

Step 2: Calculate amount to save each month

Make sure the calculator is set to END mode , then N = 12; I/Y = 9 / 12 = 0.75; PV = 0; FV = 41,974; CPT → PMT = -3,356

(Study Session 2, Module 6.2, LOS 6.f)

Related Material

SchweserNotes - Book 1

The first calculation is discounting payments to time 12 months, not today. At time 12 months, the good doctor needs $41,974 in the bank, which will earn 10% nominal monthly. Prior to that, she needs to make deposits that earn 9% nominal monthly to accumulate to the $41,974.

Thank you. The first part of the solution shows N @ 18 (12 x 1.5) - that is what’s confusing me?

Accumulation phase is months 1 to 12, sabbatical is months 13 to 30 = 18 months.

Thanks man, my mind is clearly fried i read over that 20 times. Putting away the books for the day :slight_smile:

Just an FYI:

P/Y=C/Y=12, use BGN

N=18, I= 10, PMT=2,500, CPT PV = -41,973.957

The earth will not crack open and swallow you up if you change P/Y and C/Y from 1.