Worked solution · Exam FM

SOA Exam FM Sample Question #82 Solution

This Exam FM sample reference tests Deferred Increasing Annuity. The direct discounted sum is 64,257, which is the loan value. The result agrees with the published answer key, choice D.

Independent analysis by ActuaryProof · reviewed October 6, 2026

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Independent solution

How to solve this Deferred Increasing Annuity question

Setup

Index the thirty payments by k, with payment k equal to 1,000 + 500(k − 1). The first payment occurs ten periods after valuation.

P_k=1000+500(k-1),\quad k=1,\ldots,30

Model

Discount the increasing thirty-payment stream to one period before its first payment, then apply the nine-period deferment factor shown.

L=v^9\sum_{k=1}^{30}P_kv^k

Compute

The direct discounted sum is 64,257, which is the loan value.

L=64257

Answer

The calculation gives 64,257 for deferred increasing annuity, matching published choice D.

\boxed{L=64257\quad\text{(D)}}

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Financial Mathematics Practice Examination I

30 original Exam FM questions across the syllabus, to be worked in 150 timed minutes, with a full worked solution for each one. Written for Exam FM, not copied from the SOA set. One-time $39 PDF.

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Original practice · fully worked

Original variant: deferred ten-payment increasing maintenance annuity

A facility contract pays 500 at time 4, then increases each annual payment by 100 through the tenth payment at time 13. At a 5% annual effective rate, calculate the time-0 value.

A
5,544.82
B
5,788.51
C
6,069.39
D
6,306.40
E
6,554.13

Answer and calculation

The ten discounted payments total 6069.39. The contract value is 6,069.39, corresponding to choice C.

Setup

Index each of the ten payments and map payment k to time k + 3.

P_k=500+100(k-1),\quad t_k=k+3,\quad k=1,\ldots,10

Model

Discount the increasing cash-flow vector directly to time 0, retaining the three-year deferment before the first payment.

PV=\sum_{k=1}^{10}P_k(1.05)^{-(k+3)}

Compute

The ten discounted payments total 6069.39.

PV=6069.385381

Answer

The contract value is 6,069.39, corresponding to choice C.

\boxed{PV=6069.39\quad\text{(C)}}

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How to solve this Deferred Increasing Annuity question

Setup

Model

Compute

Answer

Financial Mathematics Practice Examination I

Original variant: deferred ten-payment increasing maintenance annuity

Answer and calculation

Setup

Model

Compute

Answer

Related Exam FM solutions

Next steps for Exam FM Annuities and Non-contingent Cash Flows