An individual deposits £10,500 each year into a tax-free savings plan over a 20-year period. The payments are made monthly in arrears during the first 5 years and thereafter quarterly in arrears for the remaining 15 years. The savings plan pays compound interest at the rates of: 6% p.a. nominal convertible monthly for the first 10 years, and • 7.5% p.a. nominal convertible quarterly for the remaining 10 years. (i) Calculate the total amount of fund accumulated in the savings plan at the end of the 20- year period. (ii) At the end of the 20-year period, the individual intends to invest the total savings into a level fixed term annuity product that provides a future retirement income. Calculate the monthly income that the individual can obtain by investing the sum calculated in part (i) into a 25-year term annuity payable monthly in arrears at an effective interest rate of 4.5% p.a.

An individual deposits £10,500 each year into a tax-free savings plan over a 20-year period. The payments are made monthly in arrears during the first 5 years and thereafter quarterly in arrears for the remaining 15 years. The savings plan pays compound interest at the rates of: 6% p.a. nominal convertible monthly for the first 10 years, and • 7.5% p.a. nominal convertible quarterly for the remaining 10 years. (i) Calculate the total amount of fund accumulated in the savings plan at the end of the 20- year period. (ii) At the end of the 20-year period, the individual intends to invest the total savings into a level fixed term annuity product that provides a future retirement income. Calculate the monthly income that the individual can obtain by investing the sum calculated in part (i) into a 25-year term annuity payable monthly in arrears at an effective interest rate of 4.5% p.a.

Essentials Of Investments

11th Edition

ISBN:9781260013924

Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.

Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.

Chapter1: Investments: Background And Issues

Section: Chapter Questions

Problem 1PS

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An individual deposits £10,500 each year into a tax-free savings plan over a 20-year period. The payments are made monthly in arrears during the first 5 years and thereafter quarterly in arrears for the remaining 15 years. The savings plan pays compound interest at the rates of: ● ● (i) 6% p.a. nominal convertible monthly for the first 10 years, and 7.5% p.a. nominal convertible quarterly for the remaining 10 years. Calculate the total amount of fund accumulated in the savings plan at the end of the 20- year period. (ii) At the end of the 20-year period, the individual intends to invest the total savings into a level fixed term annuity product that provides a future retirement income. Calculate the monthly income that the individual can obtain by investing the sum calculated in part (i) into a 25-year term annuity payable monthly in arrears at an effective interest rate of 4.5% p.a.
You deposit £942 every two years start from the end of Year 4 to the end of Year 40. The interest earned is 5% convertible semiannually. At the end of Year 40, you withdraw all the accumulated money to purchase a 10-year annuity due with monthly payments of £X. Given the annuity offer an annual effective interest of 8%. Find X. Give your answer in two decimal places.
An investor pays £80 at the start of each month into a 25-year savings plan. The contributions accumulate at an effective rate of interest of 3% per half-year for the first 10 years, and at a force of interest of 6% per annum for the final 15 years. Calculate the accumulated amount in the savings plan at the end of 25 years.
Find i (the rate per period) and n (the number of periods) for the following annuity. Quarterly deposits of $500 are made for 6 years into an annuity that pays 7.5% compounded quarterly. Find i (the rate per period) and n (the number of periods) for the following annuity. Semiannual deposits of $3,100 are made for 15 years into an annuity that pays 5.9% compunded semiannually.
A loan of £97,550 is repayable by an annuity payable annually in arrears for 17 years. After the first repayment instalment, subsequent repayment instalments are to be increased by £300 each year. The repayment instalments were calculated using a rate of interest of 5.3% per annum effective. (i) Calculate, to 2 decimal places, the amount of the first repayment instalment: (ii) Calculate, to 2 decimal places, the loan outstanding after the first 10 payments: £ (iii) Immediately after the 10th repayment instalment, the interest rate on the outstanding loan is increased to 6.7% per annum effective and future instalments are kept level, equal to the instalment amount paid at the end of the 10th year. (a) Calculate the adjusted remaining term of the new loan (in whole years): (b) Calculate, to 2 decimal places, the amount of repayment (X) made in the final year: £
If the interest rate is 13% compunded semi-annually made on the account, and the obligations are given below: Deposit of P13,521 at the end of 3 and a half years. Withdrawal of P20,812 at the end of 5 years. Semi-annual deposit of a perpetuity of P1,200 starting at the end of 6 and a half years. Determine the following: a.) Present value of all the obligations made on the account. b.) Additional amount of withdrawal at the end of 5 years to balance the cash flows. NOTE: DO NOT USE EXCEL
An individual invests a series of level payments at the end of each quarter into a sinking fund, with no withdrawals allowed at the following annual levels: £1367 per annum for the first 7 years followed by £1900 per annum until the end of year 26 (inclusive). Assuming a nominal rate of interest of 5.5% pa convertible quarterly throughout the entire period, calculate, to 2 decimal places, the value of this investment at the time of withdrawal of t=31 years. (correct answer = 125712.75, ONLY formulas, no tables, please)
An individual invests a series of level payments at the end of each quarter into a sinking fund, with no withdrawals allowed at the following annual levels: £1367 per annum for the first 7 years followed by £1900 per annum until the end of year 26 (inclusive). Assuming a nominal rate of interest of 5.5% pa convertible quarterly throughout the entire period, calculate, to 2 decimal places, the value of this investment at the time of withdrawal of t=31 years. (no tables, ONLY formulas, please)
A $550.000 home loan is amortized by equal monthly payments for 25 years at a nominal rate of interest of 5.5% convertible monthly. Calculate the monthly payments of the loan and the total interest paid during the last 5 years of the loan.
Maria loaned an amomuchunt of P100,000.00 payable in 15 equal quarterly installments. The first payment was made a year after the money was borrowed. How much in each of the quarterly installments if rate of interest 10% compounded bi-monthly?
Find the accumulated value of an annuity-immediate which pays 1 at the end of each half-year for five years, if the rate of interest is 7% convertible semi-annually for the first two years, 9% convertible semi-annually for the next two years, and 8% convertible semi-annually for the last year.
(b) An annuity immediate has quarterly payments of P 5,000 for 6 years at a rate of 4% convertible semiannually. Find its present value.

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