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Tine borrowed $70 000 on a bank, a/mt. charged interest at rate of 13/2 per annum for 2 years. a) Calculate the interest paid for the 1st year. b) How much money in total did she pay back at the end of the two years?

Mathematics

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Answers

2 parts
a

Sh 8,400\text{Sh 8,400}

b

Sh 86,800\text{Sh 86,800}

Step-by-step solution

6 steps

Hili ni swali kuhusu riba rahisi (simple interest).

Kutoka kwenye swali, tunapewa:

  • Kiasi cha mkopo (Principal, PP) = Sh 70,000
  • Kiwango cha riba (Rate, RR) = 12% kwa mwaka (p.a.)
  • Muda (Time, TT) = miaka 2

Part a· 3 steps

Kokotoa riba aliyolipa kwa mwaka wa kwanza.

  1. Tumia fomula ya riba rahisi kwa mwaka mmoja.

    Fomula ya riba rahisi (II) ni:

    I=P×R×T100I = \frac{P \times R \times T}{100}

    Kwa mwaka wa kwanza, T=1T = 1 mwaka.

  2. Badilisha thamani za PP, RR, na TT kwenye fomula.

    I=70,000×12×1100I = \frac{70,000 \times 12 \times 1}{100}
  3. Fanya hesabu.

    I=840,000100I = \frac{840,000}{100} I=8,400I = 8,400

    Riba aliyolipa kwa mwaka wa kwanza ni:

    Sh 8,400\boxed{\text{Sh 8,400}}

Part b

Sh 86,800\text{Sh 86,800}

Ni kiasi gani cha pesa alicholipa jumla mwishoni mwa miaka miwili?

  1. Kokotoa riba yote kwa miaka miwili.

    Kwa riba rahisi, riba kwa kila mwaka ni sawa. Kwa hivyo, riba kwa miaka miwili ni:

    Ijumla=Riba kwa mwaka wa kwanza×2I_{jumla} = \text{Riba kwa mwaka wa kwanza} \times 2 Ijumla=8,400×2=16,800I_{jumla} = 8,400 \times 2 = 16,800

    Au, kwa kutumia fomula ya riba rahisi na T=2T=2:

    Ijumla=70,000×12×2100I_{jumla} = \frac{70,000 \times 12 \times 2}{100} Ijumla=1,680,000100I_{jumla} = \frac{1,680,000}{100} Ijumla=16,800I_{jumla} = 16,800
  2. Kokotoa jumla ya kiasi alicholipa.

    Jumla ya kiasi (AA) alicholipa ni jumla ya kiasi cha mkopo na riba yote:

    A=P+IjumlaA = P + I_{jumla}
  3. Badilisha thamani za PP na IjumlaI_{jumla} kwenye fomula.

    A=70,000+16,800A = 70,000 + 16,800 A=86,800A = 86,800

    Jumla ya kiasi alicholipa mwishoni mwa miaka miwili ni:

    Sh 86,800\boxed{\text{Sh 86,800}}
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