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
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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