Financial Calculations for the Financial Planner™
Sample Question


1. Mario wants to accumulate the capital to provide for university tuition for 4 years his son, Anthony. Mario expects Anthony's tuition to be $5,200 in the first year increasing at 11% per year. Anthony's tuition will be paid at the start of each year. Mario expects to earn 8% and to have a marginal tax rate of 42%. How much does Mario need to accumulate?
     
  (A) $21,906.32
  (B) $22,774.34
  (C) $23,509.16
  (D) $24,306.11
     
 

Answer is (B). Mario needs to accumulate $22,774.34.

(Concepts) This is a problem of solving for the net present value of an indexed annuity due. It csn be solved as a cashflow problem or a time value of money problem.

(Choice B is true.)

As a cashflow problem, the keystrokes are:

gold, CLEAR ALL Clear all entries
gold, DISP, 2 Set the number of decimal places to 2
1, gold, P/YR Enter 1 as the payments per year
5200, +/-, CFj Enter -$5,200 as CF0
×, 1.11, ->M, =, CFj Enter 1.11 in memory and (-$5,200 × 111%) as CF1
×, RM, =, CFj Enter ((-$5,200 × 111%) × 111%) as CF2
×, RM, =, CFj Enter (((-$5,200 × 111%) × 111%) × 111%) as CF3
8, ×, gold, (, 1, -, .42, =, I/YR Enter (8% × (1 - 42%)) as the interest rate
gold, NPV Solve for -$22,774.34, the target capital amount

As a cashflow problem, the shorthand solution is -$22,774.34, calculated by entering DISP = 2, P/YR = 1, CF0 = -$5,200, CF1= (CF0 × 111%), CF2 = (CF1 × 111%), CF3 = (CF2 × 111%), I/YR = (8% × (1 - 42%)), and solving for NPV.

As a time value of money problem, the keystrokes are:

gold, CLEAR ALL Clear all entries
gold, DISP, 2 Set the number of decimal places to 2
1, gold, P/YR Enter 1 as the payments per year
4, gold, ×P/YR Enter 4 as the number of years
8, ×, gold, (, 1, -, .42, gold, ), -, 11, ÷, 1.11, I/YR Enter the interest rate as (((8% × (1 - 42%)) - 11%) ÷ (1 + 11%))
5200, +/-, PMT Enter -$5,200 as the payment
0, FV Enter $0 as the future payment
gold, BEGIN Set the calculator for an annuity due
PV Solve for the present value of $22,774.34, the target capital amount.

As a time value of money problem, the shorthand solution is $22,774.34, calculated by entering DISP = 2, P/YR = 1, ×P/YR = 4, I/YR = (((8% × (1 - 42%)) - 11%) ÷ (1 + 11%)), PMT = -$5,200, FV = $0, MODE = BEGIN and solving for PV. So, Mario needs to accumulate $22,774.34.

(Keywords: education, capital required, cashflow, net present value, indexed annuity due)

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