Question

Find the future values of these ordinary annuities. Compounding occurs once a year. Do not round intermediate calculations. Round your answers to the nearest cent. $900 per year for 16 years at 8%. $   $450 per year for 8 years at 4%. $   $600 per year for 2 years at 0%. $   Rework parts a, b, and c assuming they are annuities due. Future value of $900 per year for 16 years at 8%: $   Future value of $450 per year for 8 years at 4%: $   Future value of $600 per year for 2 years at 0%: $

Answer 1

Answer to Question a),

Future Valuye Annuity = (((1+r)^n)-1)/r,

Where r = annual rate of interest, =8% or 0.08

n= number of years/periods = 16 yrs,

So the equation after putting the value=((1.08^16)-1)/0.08 = (3.42594264333413-1)/0.08

=2.42594264333413/0.08 = 30.3242830416767,

So $900 compouinded to 16 years = $900*30.3242830416767 = $27,291.854737509, rounded to 2 decimal = $27,291.85

Answer to Question b)

Future Valuye Annuity = (((1+r)^n)-1)/r,

Where r = annual rate of interest, 4% or =0.04

n= number of years/periods = 8 yrs,

So the equation after putting the value=((1.04^8)-1)/0.04

=(1.36856905040527-1)/0.04,

=0.36856905040527/0.04,

= 9.21422626013185,

So $450 compouinded to 8 years = $450*9.21422626013185 = $4,146.40181705933, rounded to 2 decimal = $4,146.40,

Answer to Question c),

  Future Valuye Annuity = (((1+r)^n)-1)/r,

Where r = annual rate of interest, 0% or =0.00

n= number of years/periods = 2 yrs,

(((1+0.00)^2)-1)/ 0.00,

So 0.00/0.00 = 1,

$600 per year for 2 years at 0%.

which means the amount will be same after 2 years so the answer is $600 after 2 years.

We can work out these a, b & c by assuming they are annuities due

Question a reworked)

annuities due means, the amounts are invested at year starting/ year 0

Future Value Annuity assuming that annuities are due.= ((((1+r)^(n+1))-1)/r)-1,

n=16, r = 8% or 0.08,

(((1.08^17)-1)/0.08)-1,

=((3.70001805480086-1)/0.08)-1,

33.7502256850108-1 = 32.7502256850108,

So $900 compouinded to 16 years assuming that annuities are due = $900*32.7502256850108,

=$29,475.20311650977, rounded to 2 decimal =$29,475.20,

Question b reworked),

Future Value Annuity assuming that annuities are due.= ((((1+r)^(n+1))-1)/r)-1,

n=8 years, r = 4% or 0.04,

So the formula after substituting the values =(((1.04^9)-1)/0.04)-1,

=9.58279531053713*$450 = $8,624.51577948342,

Rounded to 2 decimal = $8,624.52,

Question c reworked),

The amount compounded with Zero interest rate will be the same amounbt of investment at any year5 or years, the future value & present value will be same, if the interest rate is "0" or Zero.

which means the amount will be same after 2 years so the answer is $600 after 2 years.

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