Verified solution · Exam FM

SOA Exam FM Sample Question #328 Solution

This Exam FM sample reference tests Lease versus Purchase Equivalence. The purchase option's net present cost is 15000 minus the discounted 8000 resale value. Setting that equal to the 1000 down payment plus 36 monthly payments gives X = 279.29, choice C.

Independent analysis by ActuaryProof · reviewed August 4, 2026

Official wording withheld. Read the problem in the official SOA sample-question PDF. This page provides only our independently written analysis.

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Independent solution

How to solve this Lease versus Purchase Equivalence question

Setup

Use a 1% monthly rate and compare both options at purchase.

j=0.12/12=0.01

Model

The owned car's terminal value offsets purchase cost; the lease has no retained value.

15{,}000-\frac{8{,}000}{1.01^{36}}=1{,}000+Xa_{\overline{36}|0.01}

Compute

The amount financed through monthly lease payments is 8408.60 and the annuity factor is 30.10751.

X=\frac{8{,}408.60}{30.10751}=279.286

Answer

The monthly lease payment is about 279, choice C.

\boxed{X\approx279\quad\text{(C)}}

Calculator reproduction

BA II Plus keystrokes

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

36 · N; 1 · I/Y; CPT using PV of 8000 FV, then 8408.60 · PV; 0 · FV; CPT · PMT−279.29The 8408.60 amount is the purchase net cost less the lease down payment.

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Error diagnosis

Why the other letters tempt

These notes identify the calculation error associated with each wrong letter when that error is reproducible.

AChoice A discounts the 8000 retained value for an extra year, making ownership appear too expensive.
BChoice B subtracts the 1000 lease down payment after solving the annuity payment instead of before.
DChoice D omits the retained car value from the purchase alternative.
EChoice E values the 36 lease payments as beginning-of-month payments but then shifts them in the wrong direction.

Original practice · fully worked

Original variant: down payment that makes a lease equivalent

A vehicle can be bought for 20,000 and sold for 9,000 after four years. Alternatively, it can be leased with 48 end-of-month payments of 250 plus a down payment D today, with no residual value to the lessee. At a nominal 9% rate convertible monthly, determine D.

A
2,661.66
B
3,125.40
C
3,666.28
D
4,670.90
E
5,675.52

Variant answer in brief

The purchase net present cost less the present value of 48 lease payments leaves an equivalent down payment of 3666.28, choice C.

Setup

The monthly rate is 0.75%. Value ownership and the monthly lease stream at time zero.

j=0.09/12=0.0075

Model

Set the net purchase cost equal to the lease down payment plus its annuity.

20{,}000-\frac{9{,}000}{1.0075^{48}}=D+250a_{\overline{48}|0.0075}

Compute

Isolate the only immediate unknown.

D=3{,}666.2773

Answer

The equivalent down payment is 3666.28, choice C.

\boxed{D=3{,}666.28\quad\text{(C)}}

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The 2210-page Financial Mathematics Proof Manual reorganizes 461 verified Exam FM solutions by syllabus skill and adds formula proofs, error patterns, and original worked practice.

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Cite this solution

ActuaryProof. “SOA Exam FM Sample Question #328 — Verified Solution.” Verified 2026-07-31.

Source reference: official SOA sample-question PDF. Last reviewed 2026-07-31.

How to solve this Lease versus Purchase Equivalence question

Setup

Model

Compute

Answer

BA II Plus keystrokes

All 461 Exam FM sample solutions in syllabus order

Why the other letters tempt

Original variant: down payment that makes a lease equivalent

Variant answer in brief

Setup

Model

Compute

Answer

Related Exam FM solutions

Turn this solution into a complete study sequence

Cite this solution