Quantitative Methods: Arithmetic & Geometric Progressions

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Questions and Answers

What is the total amount the business owes after 2 years?

  • $10,502.50
  • $10,750.00
  • $11,025.00
  • $11,276.25 (correct)

What is the explicit formula for the nth term (total amount owed after n years) of the geometric progression?

  • 10,000(1 - 0.05)^n
  • 10,000(1 + 0.05)^n (correct)
  • 10,000(1 - 0.05)^(n-1)
  • 10,000(1 + 0.05)^(n-1)

What is the total investment after 4 years in the reinvestment scenario?

  • $7,139.23 (correct)
  • $7,326.11
  • $6,436.56
  • $6,851.19

What is the significance of geometric progression in long-term financial planning?

<p>It enables rapid growth over time (B)</p> Signup and view all the answers

What is the salary after 3 years?

<p>GH¢ 15,600 per annum (D)</p> Signup and view all the answers

What is the formula for the sum of an arithmetic series?

<p>$an(n + 1)/2$ (B)</p> Signup and view all the answers

If an investment of GH¢10000 doubles in value over a period of 6 years, what is the required interest rate?

<p>12% (D)</p> Signup and view all the answers

How long will it take for an investment of GH¢10000 to grow to GH¢20000 at an interest rate of 7.5% compounded annually?

<p>9.58 years (D)</p> Signup and view all the answers

What is the formula for the value of the investment at the end of n conversion periods when interest is compounded several times per year?

<p>Pt = P0(1 + i/m)^(mt) (A)</p> Signup and view all the answers

If GH¢50,000 is invested for three years at 8% per annum compounded semi-annually, how many conversion periods will there be?

<p>6 (B)</p> Signup and view all the answers

What is the symbol used to denote the number of conversion periods per year?

<p>m (D)</p> Signup and view all the answers

What is the interest rate applied at each conversion when interest is compounded several times per year?

<p>i/m (C)</p> Signup and view all the answers

What is the common difference between consecutive terms in the sequence 0, 5, 10, 15?

<p>5 (B)</p> Signup and view all the answers

What is the first term of the sequence 3, –1, –5, –9?

<p>3 (B)</p> Signup and view all the answers

What is the nth term of an arithmetic progression with first term a and common difference d?

<p>Tn = a + (n - 1)d (D)</p> Signup and view all the answers

What is T5 in the sequence 5, 8, 11, 14?

<p>17 (C)</p> Signup and view all the answers

What is a characteristic of an arithmetic progression?

<p>There is a common difference between consecutive terms (C)</p> Signup and view all the answers

What is the common difference in the sequence 5, 8, 11, 14?

<p>3 (C)</p> Signup and view all the answers

What is the primary difference between compounding annually and compounding semi-annually?

<p>The frequency of interest calculation (C)</p> Signup and view all the answers

If the investment is compounded daily, how much more will it earn compared to compounding annually?

<p>GH¢ 575.19 (B)</p> Signup and view all the answers

What is the value of the investment after three years when compounded annually?

<p>GH¢ 62,985.60 (A)</p> Signup and view all the answers

What is the effect of increasing the frequency of compounding on the total value of the investment?

<p>It increases the total value of the investment (D)</p> Signup and view all the answers

What is the monthly compounding value of the investment after three years?

<p>GH¢ 63,511.85 (D)</p> Signup and view all the answers

What is the difference between the monthly compounding value and the daily compounding value of the investment after three years?

<p>GH¢ 48.94 (B), GH¢ 48.94 (D)</p> Signup and view all the answers

What is the value of the fund at the end of 10 years if the annual deposit is GH¢2000 and the interest rate is 7.5% per annum?

<p>GH¢28,293.40 (C)</p> Signup and view all the answers

If the desired value of the fund at the end of 10 years is GH¢40,000, and the interest rate is 7.5% per annum, what is the required annual deposit?

<p>GH¢2,827.51 (A)</p> Signup and view all the answers

If the desired value of the fund at the end of 10 years is GH¢40,000, the interest rate is 7.5% per annum, and payments are made monthly, what is the required monthly deposit?

<p>GH¢224.81 (D)</p> Signup and view all the answers

What is the interest rate per period, i, if the interest rate per annum is 5% and payments are made quarterly?

<p>0.00625 (D)</p> Signup and view all the answers

If the interest rate is 4% per annum, and a company operates a savings scheme for its employees, what is the effective interest rate per period if payments are made monthly?

<p>0.0033 (A)</p> Signup and view all the answers

What is the value of the annuity if the quarterly payments are GH¢1500 for five years, and the interest rate is 5% per annum?

<p>GH¢76,231.40 (D)</p> Signup and view all the answers

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