Calculate the accumulation at the end of 20 years of an investment of £550 made at time t = 0, if the following apply: (i) 8% per annum nominal interest rate convertible monthly for the first 15 years, and thereafter 7% per annum effective discount rate. (ii) nominal interest rates of 6% per annum convertible three times per year for 8 years, and thereafter 6% per annum convertible every three years. (iii) 9.5% per annum force of interest for the first 10 years, and thereafter a compound interest rate at which a sum of money would increase fourfold in 20 years.
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- Calculate the amount to which £18,600 will have accumulated after 16 years given an effective rate of interest of 6.1% per annum for the first 9 years and a nominal rate of discount of 8.3% per annum convertible monthly thereafter for the remaining years. Answer: CheckFind the present value and the accumulation at the end of 10 years of a series of payments that are made up by: £200 annually in arrears during the first 3 years, £35 monthly in arrears thereafter, given that the following interest rates apply: 9% per annum effective for the first 5 years, 6% per annum nominal convertible monthly thereafter.a)Find the nominal rate per annum convertible monthly that pays an interest of £200 on an initial capital of £1,000 at the end of 3 years. b)The annual effective interest rate is 5%. Find the monthly effective discount rate. c)Explain time-consistency of compound interest.
- An investment is expected to make future returns at a rate of £1,800 per annum over the next 10- year period. Assuming a nominal discount rate of 5% per annum convertible quarterly, find the present value of the stream of future incomes if the payments are received: (i) quarterly in advance; (ii) annually in arrears; (iii) at the end of every 2 years.(a) Find the nominal rate per annum convertible quarterly that makes an interest payment of £150 on an initial capital of £1,000, at the end of 2 years. (b) Find the annual effective rate of discount equivalent to a nominal interest rate of 2% p.a. convertible semi-annually.Using an effective rate of interest of 8% per annum, calculate the CONVEXITY of the following series of payments: £400 payable after 4 years, £400 payable after 12 years, and £450 payable after 17 years.
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- A person invests a series of level payments at the end of each month into a sinking fund, with no withdrawals allowed over a 28-year period, at the following annual levels: £1655 per annum for the first 10 years followed by £2323 per annum until the end of year 20 (inclusive). Given that rate of interest is 5.9% pa convertible monthly throughout the entire period, calculate, the value of this investment at the time of withdrawal of t=28 years. no tables, only formulas, please5) Determine the present value at time 0 of payments of $1,000 at the start of each month for 5 years, starting at time 0. The nominal interest rate convertible quarterly is 4%.Calculate the present value of £22,200 due to be received in 11 years' time given an effective rate of discount of 4.3% per annum for the first 4 years, followed by a nominal rate of interest of 10.1% per annum convertible half-yearly afterwards for the remaining years. (correct answer = 9342.35, NO tables, only formulas, please)