Question

Please answer all question. If you can't answer all question then don't answer just one question. I need all and I'm having test.

12. You have started an investment club with your friend. You identified an account which you think will pay 8% per year. You are going to invest $1200 per year. Your friend is going to invest $100 per month. You plan to invest for 4 years. All else equal, which of the following is true.
13. Annuity A has a present value of $100,000 and makes 20 payments. Annuity B has a present value of $100,000 and makes 18 payments. All else equal, which one has the higher payment?
14. If annuity A has 30 payments of $500 at an interest rate of 10% and annuity B has 30 payments of $500 at an interest rate of 9%, which one has the higher present value?
18. Investment A offers a 5 annual payments of $77,000 with the first payment made today. Investment B offers 5 annual payments of $77,000 with the first payment to be made in 1 year. Which investment is worth more?

Answer 1

12. This can be solved with the help of future value of annuity.

Future value of annuity=FV factor of annuity for n periods at r rate.

FV factor of annuity=[(1+r)^{^n}-1] / [r]

If $1200 invested each year:

r=8%

n=4

FV factor of annuity=[(1+.08)^{^4}-1] / [.08]

FV factor=4.5061

FV of annuity=1200*4.5061

=5407.3344

If $100 invested each month:

r=.6667% (i.e.8/12)

n=48 (i.e.4*12)

FV factor of annuity=[(1+.006667)^{^48}-1] / [.006667]

FV factor of annuity=56.35038

Hence Future Value=100*56.35038

=5635.038

As the future value in case of monthly investment is more this option is more benificial.

Q13.

There shall be higher payment in Annuity B as the nomber of payments are less in this.

See how:

Lets suppose rate of interest is 10%

PV factor of annuity= [(1+r)^{^n}-1] / [(1+r)^{^n}*r]

Annuity A:

PV factor of annuity= [(1+.1)^{^20}-1] / [(1+.1)^{^20}*.1]

=8.5136

Present Value of annuity=PV factor*Annuity

100000=8.5136*Annuity

Annuity=100000/8.5136

Annuity=11745.96

Annuity B:

PV factor of annuity= [(1+.1)^{^18}-1] / [(1+.1)^{^18}*.1]

=8.2014

Present Value of annuity=PV factor*Annuity

100000=8.2014*Annuity

Annuity=100000/8.2014

Annuity=12193.02

Q14.

Annuity with lower interest rate shall have higher Present Value.

PV of annuity A=Annuity*PVAF @10% for 30 periods

PVAF=9.4269 (see formula as applied in question 13)

Annuity=500*9.4269

Annuity=4713.457

PV of annuity B=Annuity*PVAF @9% for 30 periods

PVAF=10.2737 (see formula as applied in question 13)

Annuity=500*10.2737

Annuity=5136.83

Q18:

As per the concept of time value of money, the amount received today has more value than amount received later.

Hence annuity starting today shall have higher value than annuity starting from one year after today.

Suppose rate of interest is 10%.

Value of annuity starting today=77000+PV of annuity of 77000 for 4 years

=77000+244079.6

=321079.6

Value of Annuity starting after 1 year=PV of annuity of 77000 for 4 years+PV today of 77000 to be received after 5 years

=244079.6+(77000/1.1^{^5})

=291890.6

Hence Value of Annuity A is more.

Feel free to ask further querries via comments.

Kindly upvote if you like my solution.

Good Luck!