Question 1 a) A company is due to receive a payment of £500,000 from a customer in 6 months’ time. To smooth its cashflows, the company would prefer to receive the payment immediately, and has agreed to transfer its entitlement to this payment to a third party (a discount house) in return for an immediate payment calculated using a rate of commercial discount of 16% per annum. How much will the immediate payment made by the discount house be? b) An investor puts £5,000 in a savings account that pays 10% simple interest at the end of each year. Compare how much the investor would have after 6 years if the money was: i. Invested for 6 years ii. Invested for 3 years, then immediately reinvested for a further 3 years. c) £250 is invested in a savings account. The nominal rate of interest convertible monthly for the first 3 months is 18% and the nominal rate of interest convertible quarterly for the next 9 months is 20%. How much is in the account at the end of the year? d) Calculate the present value as at 1 March 2005 of a series of payments of £1,000 payable on the first day of each month from April 2005 to December 2005 inclusive, assuming a rate of interest of 6% pa convertible monthly. e) The force of interest is given by: ?(?) = { 0.08 − 0.001? 0 ≤ ? < 3 0.025? − 0.04 3 ≤ ? < 5 0.03 ? ≥ 5 Calculate the present value at time 2 of a payment of £1,000 at time 10.
Question 1
a) A company is due to receive a payment of £500,000 from a customer in 6 months’ time.
To smooth its cashflows, the company would prefer to receive the payment
immediately, and has agreed to transfer its entitlement to this payment to a third
party (a discount house) in return for an immediate payment calculated using a rate
of commercial discount of 16% per annum.
How much will the immediate payment made by the discount house be?
b) An investor puts £5,000 in a savings account that pays 10% simple interest at the end
of each year. Compare how much the investor would have after 6 years if the money
was:
i. Invested for 6 years
ii. Invested for 3 years, then immediately reinvested for a further 3 years.
c) £250 is invested in a savings account. The nominal rate of interest convertible monthly
for the first 3 months is 18% and the nominal rate of interest convertible quarterly for
the next 9 months is 20%. How much is in the account at the end of the year?
d) Calculate the present value as at 1 March 2005 of a series of payments of £1,000
payable on the first day of each month from April 2005 to December 2005 inclusive,
assuming a rate of interest of 6% pa convertible monthly.
e) The force of interest is given by:
?(?) = {
0.08 − 0.001? 0 ≤ ? < 3
0.025? − 0.04 3 ≤ ? < 5
0.03 ? ≥ 5
Calculate the present value at time 2 of a payment of £1,000 at time 10.
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