Kpl.2.2

233

a)

$0{,}02\cdot0{,}70=0{,}014=1{,}4\%$

b)

$K=k\cdot q^n=550\cdot1{,}014^4=581{,}452...\approx581{,}45€$

235

$K=12\ 000\cdot1{,}025^7=14264{,}22904\approx15264{,}23€$

237

a)

Väärin, 1,06%

b)

Väärin, suurempi euron määrä

c)

Oikein

239

240

$K=k\cdot q^n$

a)

$K=800$

$q=1{,}0255$

$n=2$

b)

$800=k\cdot1{,}0255^2$
$k=\frac{800}{1{,}0255^2}=760{,}709...\approx760{,}71€$

241

a)

$k=10$

$K=10{,}61$
$n=3$

b)

$10{,}61=10\cdot q^3$
$q=\sqrt[3]{\frac{10{,}61}{10}}$
$q=1{,}01993...\approx1{,}0199$

c)

$1{,}99\%$

242

$K=900$

$k=700$
$q=1{,}038$
$n=?$
$900=700\cdot1{,}038^n$
$1{,}038^n=\frac{900}{700}$
$n=\log_{1{,}038}\left(\frac{900}{700}\right)=6{,}738...\approx7\left(a\right)$

v: 7 vuotta

244

$5000=k\cdot1{,}0245^6$

$k=\frac{5000}{1{,}0245^6}=4324{,}124...\approx4324{,}12€$

246

Peetu

$1000\cdot1{,}009^2=1018{,}081$

$1000\cdot1{,}015^2=1030{,}225$
$1018{,}081+1030{,}225=2038{,}306\approx2038{,}31€$
$+38{,}31€$

Petra

$2000\cdot1{,}013^1=2026$

$2026\cdot1{,}001^1=2028{,}026\approx2028{,}03€$
$+28{,}03€$

v: Peetun

247

a)

Alkupääoma on k=1000€

Nettokorkokanta on 0,71·1,50%=1,065%, joten korkokerroin on q=

$K=k\cdot q^n=1000€\cdot1{,}01065^{10}=1111{,}751...€\approx1111{,}75€$

b)

$1000\cdot1{,}01065^n=2000$
$\log_{1{,}01065}\left(\frac{2000}{1000}\right)=65{,}43...\approx66\left(a\right)$

252

255

256

259

260