Question

2. Interest Rates You are saving for retirement. To live comfortably, you decide you will need to save $1 million by the time you are 65. Today is your 23rd birthday, and you decide, starting today and continuing on every birthday up to and including your 65th birthday, that you will put the same amount into a savings account. If the interest rate is 5%, how much must you set aside each year to make sure that you will have $1 million in the account on your 65th birthday?

Answer 1

Answers:

Question no. 2: Interest Rates

The investment plan involves an annuity due (periodical payments at the beginning).

Given, Future Value of Annuity=$1 Million, Interest rate=5% and number of payments= 65-23= 42.

Amount required to be set aside every year = $7042.58

Details of computation as follows:

A B 1 Annuity Due Payment C D E Payments at the beginning of each period 2 8 3 Amount of periodical payments is calculated using the formula PMT=FV*[r/(1+r)^n-1]*[1/(1+r)] 4 Where PMT= Periodical payments required, 5 FV= Future value required 6 n= Number of payments. 7 r= Rate of interest per period in decimals All amounts in $ Given that 10 Future value required FV= 1000000 No. of years (N) 11 Rate of interest (% p.a)=R= 5 No. of payments a year (t) 12 13 Calculations: Formula Cell reference Value 15 Interest rate per period in decimals (r)= R/(100*t) D11/(100*G11) 0.05 16 No. of periods (n)= N*t G11*G11 42 (1+r)= 1+G15 1.05 18 (1+r)^n-1= G174G16 6.761587555 r/(1+r)^n-1 G15/G18 0.007394713 1/(1+r) 1/ 17 0.952380952 21 Periodical payment required (PMT)= FV*[r/(1+r)^n-1]*[1/(1+r)] D10*G19*G20 7042.583895 Rounded to $7,042.58 14 17 19 20 22

Question 6 on Bond Valuation

(a) Treasury Bond.

Given, Coupon rate=8.4% per year, Frequency Semiannual, Term to maturity= 5 years and YTM=7.5%.

Let Face Value be $1,000.

Then semiannual interest payment= $1,000*8.4%/2 = $42

Price of the bond is the present value of the cash flow streams associated. Calculated using the PV function of Excel, the price is $1036.957543

Screen shot of function arguments as follows:

Function Arguments 6 = 0.0375 = 10 NONAEEM Rate 7.5%/2 Nper Pmt 42 Fv 1000 Type 8 6 = 1000 - 0 = -1036.957543 Returns the present value of an investment: the total amount that a series of future payments is worth now. Type is a logical value: payment at the beginning of the period = 1; payment at the end of the period = 0 or omitted. Formula result = ($1,036.96) Help on this function OK Cancel

As the face value is assumed at $1,000, the price corresponds to 103.695754% of Face Value.

(b) BBB rated Corporate Bond.

Given, Coupon rate=8.4% per year, Frequency Semiannual, Term to maturity= 5 years and YTM=9%.

Let Face Value be $1,000.

Then semiannual interest payment= $1,000*8.4%/2 = $42

Price of the bond is the present value of the cash flow streams associated. Calculated using the PV function of Excel, the price is $976.2618455

Screen shot of function arguments as follows:

F А Function Arguments PV * E Rate 9%/2 Nper 10 Pmt 42 Fv 1000 Type of = 0.045 = 10 = 42 = 1000 * = -976.2618455 Returns the present value of an investment: the total amount that a series of future payments is worth now. Type is a logical value: payment at the beginning of the period = 1; payment at the end of the period = 0 or omitted. Formula result = -976.2618455 Help on this function OK Cancel

As the face value is assumed at $1,000, the price corresponds to 97.626185% of Face Value.