MAT-144 · Mathematical Reasoning Topic 07 · Taxes & Stocks
Topic 07 · Review · Q22

Comparing monthly payments for subsidized and unsubsidized student loans

Two-part: same loan, but for the unsubsidized case the in-school years accrue simple interest before repayment starts. Compute the monthly for both.

01 Worked Example Video

Every step of Comparing monthly payments for subsidized and unsubsidized student loans explained on video. Pause anywhere; the embed scrolls independently of the page.

YOUTUBE
02 What This Looks Like on ALEKS

ALEKS randomizes the numbers each attempt, but the question shape stays the same. Here are three example versions you might see.

Marco's student loan

Marco took out a $14,000 student loan at 6.8% APR with 3 years left in college. Repayment: 10 years after graduation. In-school accrual is simple interest.

Find Marco’s unsubsidized monthly payment. Type just the number, rounded to the nearest cent.

M<sub>unsub</sub> = $
Naomi's student loan

Naomi took a $9,500 student loan at 5.5% APR with 2 years left in college. Repayment: 10 years. In-school accrual is simple interest.

Find Naomi’s unsubsidized monthly payment. Type just the number, rounded to the nearest cent.

M<sub>unsub</sub> = $
Tariq's student loan

Tariq took a $22,000 student loan at 7.2% APR with 4 years left in college. Repayment: 10 years. In-school accrual is simple interest.

Find Tariq’s unsubsidized monthly payment. Type just the number, rounded to the nearest cent.

M<sub>unsub</sub> = $
Heads up: Your ALEKS version will use different numbers. The numbers in the practice below are different too — that way you're exercising the move, not memorizing one answer.
03 The Rule
Subsidized: Prepay = original P government pays the in-school interest
Unsubsidized: Prepay = P + P·r·tschool student is charged simple interest during school
Same loan, same rate, same repayment term. The only difference: for the unsubsidized case, the in-school years accrue simple interest that gets added to the principal before repayment starts. Then the amortization formula runs on the bigger P.
Common slips
(1) Used the same P for both. That’s the subsidized case only. For unsub, grow P first: Punsub = P + Prt (in-school). (2) Compounded the in-school interest. The prompt says simple — no compounding during school. (3) Ran the amortization on the wrong t. t in the formula is the repayment term, not the in-school years.
04 Practice — Step by Step
Practice this problem step by step
A $10,000 student loan at 6% APR, taken with 2 years left in college. Repayment: 10 years after graduation. Compare subsidized vs unsubsidized monthly payments.
Step 1

Subsidized monthly payment

Subsidized: Prepay = $10,000. With r/12 = 0.005, n = 120, compute the monthly. Round to the nearest cent.
M<sub>sub</sub> = $
Step 2

In-school simple interest

Unsubsidized: the loan accrues simple interest during the 2 in-school years. Compute I = P × r × tschool = 10,000 × 0.06 × 2.
I<sub>school</sub> = $
Step 3

Adjusted principal for unsub

Add the in-school interest to the original principal: 10,000 + 1,200. This is the P that goes into the amortization formula.
P<sub>unsub</sub> = $
Step 4

Unsubsidized monthly payment

Same formula, but P = $11,200. Compute the unsubsidized monthly. Round to the nearest cent.
M<sub>unsub</sub> = $
Step 5

The monthly gap

How much more does the unsubsidized loan cost per month? Subtract: $124.34 − $111.02.
gap = $
Q21 Q23
MAT-144 · TOPIC 07 · REVIEW · Q22 OF 38