Independent solution

How to solve this Deferred Perpetuities question

Setup

Setup

The monthly rate is 1%. There are 120 beginning-of-month deposits, followed by 120 months with no deposits.

j=0.12/12=0.01j=0.12/12=0.01

Model

Model

Accumulate the annuity-due deposits to time 10, then carry that fund forward another ten years.

F20=500s¨120‾∣0.01(1.01)120F_{20}=500\ddot{s}_{\overline{120}|0.01}(1.01)^{120}

Compute

Compute

The fund at time 20 is 383,404.42. Because the first withdrawal occurs immediately, its value is a perpetuity-due, X divided by d.

F20=383404.42F_{20}=383404.42
d=0.011.01d=\frac{0.01}{1.01}
X=F20d=3796.08X=F_{20}d=3796.08

Answer

Answer

The monthly charitable payment is about 3,796, so the answer is D.

X≈3796(D)\boxed{X\approx3796\quad\text{(D)}}

Calculator reproduction

BA II Plus keystrokes

Check END/BGN, period, sign, TVM, and cash-flow setup

  1. 2ND · CLR TVM · 2ND · PMT · 2ND · SETBGN modeUse monthly periods with the periodic rate entered directly.
  2. 120 · NN = 120
  3. 1 · I/YI/Y = 1
  4. 0 · PVPV = 0
  5. 500 · +/- · PMTPMT = -500
  6. CPT · FVFV = 116,169.54
  7. 120 · N · 1 · I/Y · 116169.54 · +/- · PV · 0 · PMT · CPT · FVFV = 383,404.42Second ten-year accumulation period.