Time value of money calculations

Question 1

Future value of £10,000, interest rate 4%, term 6 years

Answer 1

Calculation is FV = PV (1+r)
PV = £10,000, r = 0.04, n = 6
FV = £10,000 (1.04)
FV = £10,000 (1.265)
FV = £12,650

Question 2

Future value of £27,987, interest rate 6.1%, term 9 years

Answer 2

Calculation is FV = PV (1+r)
PV = £27,987, r = 0.061, n =9
FV = £27,987 (1.061)
FV = £27,987 (1.704)
FV = £47,690

Question 3

Future value of £8900, interest rate 1.2%, term 16 years

Answer 3

Calculation is FV = PV (1+r)
PV = £8900, r = 0.012, n = 16
FV = £8900 (1.012)
FV = £8900 (1.210)
FV = £10,769

Question 4

Present value for future value of £72,000, interest rate 3.35%, term 12 years

Answer 4

Calculation is FV = PV (1+r)
£72,000 = PV (1+0.0335)
£72,000 = PV (1.0335)
£72,000 = PV (1.485)
£72,000 / 1.485 = PV
PV = £48,484.85

Question 5

Present value for future value of £19,820, interest rate 6%, term 29 years

Answer 5

Calculation is FV = PV (1+r)
£19,820 = PV (1+0.06)
£19,820 = PV (1.06)
£19,820 = PV (5.418)
£19,820 / 5.418 = PV
PV = £3658.18

Question 6

Interest rate for future value of £9200, present value £8000, term 9 years

Answer 6

Calculation is FV = PV (1+r)
FV = £9200, PV = £8000, n = 9
£9200 = £8000 (1+r)
£9200 / £8000 = (1+r)
£1.15 = (1+r)
9 √ £1.15 = 1 + r
1.0157 = 1 + r
r = 0.0157
r = 1.57%

Question 7

Interest rate for future value of £11,260, present value £7000, term 15 years

Answer 7

Calculation is FV = PV (1+r)
FV = £11,260, PV = £7000, n = 15
£11,260 = £7000 (1+r)
£11,260 / £7000 = (1+r)
£1.61 = (1+r)
15 √ £1.61 = 1 + r
1.0323 = 1 + r
r = 0.323
r = 3.23%

Question 8

Effective rate of interest for 4% compounded quarterly

Answer 8

Effective rate = (1 + r/n) -1
Effective rate = (1 + 0.04/4) -1
Effective rate = (1.01) – 1
Effective rate = (1.0406) – 1
Effective rate = 0.0406 or 4.06%

Question 9

Effective rate of interest for 8% compounded monthly

Answer 9

Effective rate = (1 + r/n) -1
Effective rate = (1 + 0.08/12) -1
Effective rate = (1.0067) – 1
Effective rate = (1.0834) – 1
Effective rate = 0.0834 or 8.34%

Question 10

Future value for a series of regular payments of £3000 per annum, paid for
14 years at 6% interest

Answer 10

FV = P (((1+r) -1) / r)
FV = £3000 (((1+0.06) -1) / 0.06)
FV = £3000 (((2.261)-1) / 0.06)
FV = £3000 ((1.261) / 0.06)
FV = £3000 (21.017) · FV = £63,051

Question 11

Future value for a series of regular payments of £2500 per annum, paid for 8
years at 3% interest

Answer 11

FV = P (((1+r) -1) / r)
FV = £2500 (((1+0.03) -1) / 0.03)
FV = £2500 (((1.267)-1) / 0.03)
FV = £2500 ((0.267) / 0.03)
FV = £2500 (8.9)
FV = £22,250