Question

Determine the future values utilising a time preference rate of 9 per cent:

(i) The future value of Rs 15,000 invested now for a period of four years.

(ii) The future value at the end of five years of an investment of Rs 6,000 now and of an investment of Rs 6,000 one year from now.

(iii) The future value at the end of eight years of an annual deposit of Rs 18,000 each year.

(iv) The future value at the end of eight years of annual deposit of Rs 18,000 at the beginning of each year.

(v) The future values at the end of eight years of a deposit

of Rs 18,000 at the end of the first four years and

withdrawal of Rs 12,000 per year at the end of year

five through seven.​

Answer 1

The future values utilizing a time preference rate of 9 per cent is determined as follows:

We are given Time preference rate = 9%

(i)

A. Investment                                                                    15,000

B. Period (years)                                                                        4

C. Compound value factor at 9% for 4 years                    1.4116

D. Compound value at the end of 4 years (A × C)

    : 15,000(1.09)⁴ = 15,000 × 1.4116                                    21,174

(ii)                                                                          Now     After 1 year

A. Investment                                                      6,000        6,000

B. Period (end of year)                                           5               5

C. Compounding periods                                      5               4

D. Compound value factor (lump sum)             1.5386        1.4116

E. Compound value (A × D)

    : 6,000(1.09)⁵ = 6000 × 1.5386                    9,231.6

    : 6,000(1.09)⁴ = 6000 × 1.4116                                         8,469.6

(iii)

A. Annual investment (end of the year)                             18,000

B. Period (years)                                                                           8

C. Compound value factor (annually)                               11.0285

D. Compound value at the end of 8 years (A × C)

    : 18,000[(1.09)⁸ - 1]/0.09 = 18,000 × 11.0285                1,98,513

(iv)

A. Annual Investment (beginning of the year)                  18,000

B. Periods (years)                                                                        8

C. Compound value factor (annuity due)                         12.0210

D. Compound value at the end of 8 years (A × C)           216,378

(v)                                                                                 Withdrawal Balance

A. Annual investment for 4 years                  18,000

B. Compound value at the end of 4 years

    : 18,000[(1.09)⁴ - 1]/0.09                           82,316.32

C. Compound value at the end of 5 years

    : (82,316.32 × 1.09) – 12,000                   89,724.79   12,000   77,724,79

D. Compound value at the end of 6 years

    : (77,724,79 × 1.09) – 12,000                   84,720.02  12,000   72,720.02

E. Compound value at the end of 7 years

    : (72,720.02 × 1.09) – 12,000                  79,264.82   12,000   67,264.82

F. Compound value at the end of 8 years

    : (67,264.82 × 1.09) – 12,000                  73,318.66      0.00     73,318.66

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Answer 2

(i) The future value of Rs 15,000 invested now for a period of four years can be calculated using the formula:

FV = PV x (1+r)^n

Where, FV is the future value, PV is the present value, r is the interest rate, and n is the number of years.

Substituting the given values, we get:

FV = 15,000 x (1+0.09)^4

FV = 15,000 x 1.411

FV = Rs 21,165

Therefore, the future value of Rs 15,000 invested now for a period of four years at a time preference rate of 9% is Rs 21,165.

(ii) The future value at the end of five years of an investment of Rs 6,000 now and of an investment of Rs 6,000 one year from now can be calculated using the same formula:

FV = PV x (1+r)^n

The first investment of Rs 6,000 has a n value of 5, and the second investment of Rs 6,000 has a n value of 4. Substituting the given values, we get:

FV = 6,000 x (1+0.09)^5 + 6,000 x (1+0.09)^4

FV = 6,000 x 1.5386 + 6,000 x 1.411

FV = Rs 14,011.60 + Rs 12,966

FV = Rs 26,977.60

Therefore, the future value at the end of five years of an investment of Rs 6,000 now and of an investment of Rs 6,000 one year from now at a time preference rate of 9% is Rs 26,977.60.

(iii) The future value at the end of eight years of an annual deposit of Rs 18,000 each year can be calculated using the formula:

FV = A x ((1+r)^n - 1) / r

Where, A is the annual deposit, r is the interest rate, and n is the number of years. Substituting the given values, we get:

FV = 18,000 x ((1+0.09)^8 - 1) / 0.09

FV = 18,000 x 14.451

FV = Rs 2,61,118

Therefore, the future value at the end of eight years of an annual deposit of Rs 18,000 each year at a time preference rate of 9% is Rs 2,61,118.

(iv) The future value at the end of eight years of annual deposit of Rs 18,000 at the beginning of each year can be calculated using the formula:

FV = A x ((1+r)^n - 1) / r x (1+r)

Where, A is the annual deposit, r is the interest rate, and n is the number of years. Substituting the given values, we get:

FV = 18,000 x ((1+0.09)^8 - 1) / 0.09 x (1+0.09)

FV = 18,000 x 15.412

FV = Rs 2,77,214

Therefore, the future value at the end of eight years of annual deposit of Rs 18,000 at the beginning of each year at a time preference rate of 9% is Rs 2,77,214.

(v) The future values at the end of eight years of a deposit of Rs 18,000 at the end of year.

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