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Worked solution

Model an inheritance using principal and simple interest

[Banking] Stephen inherited $50,000 and put part in an investment-savings account, part in bonds and the rest in an investment fund. After one year he received a total of $3,240 in simple interest. The account paid 6% annually, bonds 7% and the fund 8%. There was $12,000 more invested in bonds than in the fund. Find the amount invested in each category.

CJC · Lecture · Example 4 [Banking; second printed Example 4]

Define and formulate

Let x,y,zx,y,z be the amounts in dollars in the account, bonds and fund. Total principal gives x+y+z=50000x+y+z=50000. Total one-year simple interest gives 0.06x+0.07y+0.08z=32400.06x+0.07y+0.08z=3240. The difference gives y−z=12000y-z=12000. These are the three interpretations identified by the source’s equation callout.

How did this part go?

Solve and interpret

The printed calculator solution is x=30000x=30000, y=16000y=16000, z=4000z=4000. Check the principal: 30000+16000+4000=5000030000+16000+4000=50000; interest: 1800+1120+320=32401800+1120+320=3240; difference: 16000−4000=1200016000-4000=12000. Thus Stephen invested $30,000 in the account, $16,000 in bonds and $4,000 in the fund.

How did this part go?

Check the modelling assumption

The lecturer asks what assumption the model makes; the suggested answer is constant interest rates. The source also stresses that models are approximations and simplifications with assumptions and limitations. These fixed one-year simple-interest equations describe the stated model; they do not incorporate changing rates or additional financial effects.

How did this part go?

Common mistakes

The 6%, 7% and 8% apply to different principal amounts; do not add the percentages or confuse interest with principal.

Solution notes

Student and Teacher PDF page 7 compared. Student printed page 167; Teacher visible footer 167 (underlying extracted label 167). No marks are printed.

The source prints Example 4 a second time, then continues with Example 6. This banking identity is distinct from the inconsistent-system Example 4; no missing Example 5 is invented.

Read the hint