Verified solution · Exam FM

SOA Exam FM Sample Question #210 Solution

This Exam FM sample reference tests Reinvestment of Loan Payments. The loan payment is 1,490.29. Reinvesting the ten payments at 10% produces 23,751.46, so interest above the original 10,000 is 13,751.46; 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 Reinvestment of Loan Payments question

Setup

Determine the level annual payment from the lender's 8% loan valuation.

P=\frac{10000}{a_{\overline{10}|0.08}}=1490.29

Model

Each payment is deposited when received, so the time-10 reinvestment value is an annuity-immediate accumulated at 10%.

F_{10}=1490.29s_{\overline{10}|0.10}

Compute

The reinvestment account reaches 23,751.46. Subtract the lender's original 10,000 outlay to measure total interest earned.

F_{10}=23751.46

I=23751.46-10000=13751.46

Answer

Total interest rounds to 13,751, which is choice C.

\boxed{I\approx13751\quad\text{(C)}}

Calculator reproduction

BA II Plus keystrokes

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

2ND · CLR TVMTVM worksheet clearedUse END mode and annual periods.
10 · NN = 10
8 · I/YI/Y = 8
10000 · PVPV = 10,000
0 · FVFV = 0
CPT · PMTPMT = -1,490.29
10 · I/Y · 0 · PV · 1490.2949 · +/- · PMT · CPT · FVFV = 23,751.46Revalue the received end-of-year payments at 10%.

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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 uses the 8% loan rate to accumulate the received payments. The reinvestment account earns 10%.
BChoice B is close to subtracting the sum of payments rather than the lender's original 10,000 investment.
DChoice D treats the received payments as beginning-of-year deposits, giving each one an extra year of 10% interest.
EChoice E combines loan interest and reinvestment interest without first expressing both through the common time-10 account value.

Original practice · fully worked

Original variant: reserve yield needed for a target fund

A finance company advances 15,000 and receives six equal year-end repayments valued at a 6% annual effective rate. Each repayment is immediately placed in a reserve. Determine the annual effective reserve yield required for the six receipts to accumulate to 24,000 at time 6.

A
8.00%
B
9.50%
C
10.77%
D
12.00%
E
13.50%

Variant answer in brief

The financing terms set each receipt at 3,050.44. Solving 3,050.44 times the six-period accumulation factor equal to 24,000 gives a reserve yield of 10.77%, choice C.

Setup

Set the six repayments by valuing them at the 6% financing rate.

P=\frac{15000}{a_{\overline{6}|0.06}}=3050.44

Model

Let j be the reserve yield. The receipts form an annuity-immediate accumulated to time 6.

24000=3050.44s_{\overline{6}|j}

Compute

Solving the monotone accumulation equation gives j equal to 0.1077339.

\frac{(1+j)^6-1}{j}=\frac{24000}{3050.4394}

j=0.1077339

Answer

The reserve must earn approximately 10.77% annually, so choice C is correct.

\boxed{j\approx10.77\%\quad\text{(C)}}

Calculator reproduction

BA II Plus keystrokes

2ND · CLR TVMTVM worksheet clearedUse END mode and annual periods.
6 · NN = 6
6 · I/YI/Y = 6
15000 · PVPV = 15,000
0 · FV · CPT · PMTPMT = -3,050.44
6 · N · 0 · PV · 3050.4394 · +/- · PMT · 24000 · FV · CPT · I/YI/Y = 10.7734Keep END mode for the six year-end reserve deposits.

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Cite this solution

ActuaryProof. “SOA Exam FM Sample Question #210 — Verified Solution.” Verified 2026-07-31.

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

How to solve this Reinvestment of Loan Payments 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: reserve yield needed for a target fund

Variant answer in brief

Setup

Model

Compute

Answer

BA II Plus keystrokes

Related Exam FM solutions

Turn this solution into a complete study sequence

Cite this solution