Verified solution · Exam FM

SOA Exam FM Sample Question #130 Solution

This Exam FM sample reference tests Loan Amortization. The first 24 monthly borrowings accumulate for two additional years at the higher rate, while the last 24 accumulate only at the higher rate; their combined value is 55,762, 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 Loan Amortization question

Setup

Split the monthly advances at the time the nominal rate changes after two years.

j_1=0.06/12,\qquad j_2=0.08/12

Model

The first 24 advances accumulate under the first rate to month 24 and then under the second rate for another 24 months; the later advances use only the second rate.

B_{48}=1000s_{\overline{24}|\,j_1}(1+j_2)^{24}+1000s_{\overline{24}|\,j_2}

Compute

The two accumulated blocks contribute approximately 29,829 and 25,933.

B_{48}=1000[25.4320(1.1729)+25.9332]=55762

Answer

Their total balance is about 55,762 immediately after the last advance, matching choice C.

\boxed{B_{48}=55762\quad\text{(C)}}

Calculator reproduction

BA II Plus keystrokes

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

2nd CLR TVM; 2nd I/Y; 1 ENTER; ↓; 1 ENTER; 2nd CPT; 2nd PMT; if BGN is displayed, 2nd ENTER; 2nd CPT; 24 N; 0.5 I/Y; 0 PV; 1000 +/- PMT; CPT FVFV = 25431.96END mode; I/Y is the monthly rate for the first 24 receipts, and deposits are entered negative.
2nd CLR TVM; 2nd I/Y; 1 ENTER; ↓; 1 ENTER; 2nd CPT; 2nd PMT; if BGN is displayed, 2nd ENTER; 2nd CPT; 24 N; 0.6666667 I/Y; 25431.96 +/- PV; 1000 +/- PMT; CPT FVFV = 55762.02END mode; I/Y is the monthly rate for the second 24 months. The starting fund and new receipts share the negative sign.

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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 is inconsistent with the two-block monthly accumulation across the rate change; no distinct standard single-step error producing it is identifiable.
BChoice B is inconsistent with the two-block monthly accumulation across the rate change; no distinct standard single-step error producing it is identifiable.
DChoice D is inconsistent with the two-block monthly accumulation across the rate change; no distinct standard single-step error producing it is identifiable.
EChoice E is inconsistent with the two-block monthly accumulation across the rate change; no distinct standard single-step error producing it is identifiable.

Original practice · fully worked

Original variant: staggered microgrants under changing monthly rates

A cooperative receives 500 at each month-end for 24 months. The account earns 0.4% per month for months 1–12 and 0.6% per month for months 13–24. Find the balance immediately after the final receipt.

A
12,000.00
B
12,400.00
C
12,792.29
D
13,100.00
E
13,500.00

Variant answer in brief

Accumulating the first and second 12-payment blocks gives 12,792.29, choice C.

Setup

The first year's receipts experience both rate regimes, while the second year's receipts experience only the later rate.

B_{24}=500s_{\overline{12}|\,0.004}(1.006)^{12}+500s_{\overline{12}|\,0.006}

Model

Accumulate each 12-payment block to month 24 and add the two values.

B_{24}=500(12.26785)(1.074424)+500(12.40608)

Compute

The first block carried through the second year plus the second block totals 12,792.2911.

B_{24}=12792.2911

Answer

The final balance is 12,792.29, which is choice C.

\boxed{B_{24}=12792.29\quad\text{(C)}}

Calculator reproduction

BA II Plus keystrokes

2nd CLR TVM; 2nd I/Y; 1 ENTER; ↓; 1 ENTER; 2nd CPT; 2nd PMT; if BGN is displayed, 2nd ENTER; 2nd CPT; 12 N; 0.4 I/Y; 0 PV; 500 +/- PMT; CPT FVFV = 6133.78END mode; I/Y is the first-stage monthly rate and deposits are negative.
2nd CLR TVM; 2nd I/Y; 1 ENTER; ↓; 1 ENTER; 2nd CPT; 2nd PMT; if BGN is displayed, 2nd ENTER; 2nd CPT; 12 N; 0.6 I/Y; 6133.78 +/- PV; 500 +/- PMT; CPT FVFV = 12792.29END mode; I/Y is the second-stage monthly rate. The starting fund and new receipts share the negative sign.

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Cite this solution

ActuaryProof. “SOA Exam FM Sample Question #130 — Verified Solution.” Verified 2026-07-31.

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

How to solve this Loan Amortization 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: staggered microgrants under changing monthly rates

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