Quantitative Methods: Arithmetic & Geometric Progressions

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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?

It enables rapid growth over time Signup and view all the answers

What is the salary after 3 years?

GH¢ 15,600 per annum Signup and view all the answers

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

$an(n + 1)/2$ 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?

12% 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?

9.58 years 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?

Pt = P0(1 + i/m)^(mt) 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?

6 Signup and view all the answers

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

m Signup and view all the answers

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

i/m Signup and view all the answers

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

5 Signup and view all the answers

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

3 Signup and view all the answers

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

Tn = a + (n - 1)d Signup and view all the answers

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

17 Signup and view all the answers

What is a characteristic of an arithmetic progression?

There is a common difference between consecutive terms Signup and view all the answers

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

3 Signup and view all the answers

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

The frequency of interest calculation Signup and view all the answers

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

GH¢ 575.19 Signup and view all the answers

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

GH¢ 62,985.60 Signup and view all the answers

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

It increases the total value of the investment Signup and view all the answers

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

GH¢ 63,511.85 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?

GH¢ 48.94 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?

GH¢28,293.40 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?

GH¢2,827.51 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?

GH¢224.81 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?

0.00625 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?

0.0033 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?

GH¢76,231.40 Signup and view all the answers