Financial Calculations Test 1 Solutions and Worked Examples

School: Dawson College - Course: ACCOUNTING MISC - Subject: Accounting

DAWSON COLLEGE FINANCIAL CALCULATIONS 2022 TEST 1 Problem 1.(2 points) Calculate (write down the steps of your calculation): (8 + 2*2)ˆ2/4/3-( 4 + 2*2ˆ2/4*2) Solution: (8 + 2*2)ˆ2/4/3-(4 + 2*2ˆ2/4*2) =(8 + 4)ˆ2/4/3-( 4 + 2*4/4*2) =(12)ˆ2/4/3-( 4 + 8/4*2) = 144/4/3-( 4 + 2*2) = 36/3-( 4 + 4) = 12-8 = 4 Problem 2.Simplify the following expressions (show your work): (a)(2 points) 1a4· a x4a 3 -2 Solution: 1a4·ax4a3-2 =1a4 · x4a 3 a 2 =1a4·x4 · a 3 a1 2 =1 a4 ·(x4·a 3-1 ) 2 =1 a4 ·(x4a 2 ) 2 = (x4a 2 ) 2 a4 = (x4)2·(a2) 2 a4 = x4·2·a 2·2 a4 = x8a 4 a4 =x8 · a 4 a4 =x8

(b)(2 points) 2(a-1)(2a+ 3)-4(a2 -1) Solution: 2(a-1)(2a+ 3)-4(a2-1) = 2(2a2+ 3a-2a-3)-4(a2 -1) = 2(2a2+a-3)-(4a2 -4) = 4a2+ 2a-6-(4a2 -4) = 4a2+ 2a-6-4a2 + 4 = 2a-2 Problem 3.(2 points) Solve the given equation. Do not convert to decimal numbers but rather perform exact calculations with fractions. Reduce the final answer to lowest terms. 2x-23(2x-1) =209-3 4 (3-2x) Solution:Lowest Common Denominator = 36. One can multiply both sides of the equation by 36 to make all coefficients integers. 72x-24 (2x-1) = 80-27 (3-2x) 72x-48x+ 24 = 80-81 + 54x 72x-48x-54x= 80-81-24 (72-48-54)x= 80-81-24 -30x=-25 x=2530= 5 6 Alternatively: 2x-23(2x-1) =209-3 4 (3-2x) 2x-43x+23=209-94+6 4 x 2x-43x+23=209-94+3 2 x 2x-43x-32x=209-94- 2 3 2-43-32x=209-94- 2 3 126-86-96x=8036-8136- 24 36 -56x=- 25 36 x=2536·65=5·56·6·65= 5 6

Problem 4. (a)(2 points) Solve forn(i.e. isolate and expressnin terms ofP, Fandi) P= F (1 +i ) n Solution: P=F(1 +i)n=⇒P(1 +i)n=F(1 +i ) n (1 +i)n=⇒P(1 +i)n=F=⇒(1 +i)n = F P =⇒ln(1 +i)n = lnFP=⇒nln(1 +i) = ln F P =⇒n=ln (F P) ln(1 +i)or alternaitivelyn= ln(F)-ln(P) ln(1 +i ) (b)(1 point) Using the result from part (a), calculatenforP= 1000, F= 1575.45, i= 0.033