Answer to Question #155346 in Financial Math for Bonevie tutor

Question

Deferred annuities

1.) Annual payments of P8,000 for 12 years that will start 5 years from now

2.) Quarterly payments of P5,000 for 8 years that will start 2 years from now

3.) Annual payments of P13,500 for 20 years that will start 10 years from now

4.) A certain fund is to be established today in order to pay for the P5,000 worth of monthly rent for a commercial space. They payments for rent will start next year and the fund must be sufficient to pay for the monthly rental for 2 years, the amount that must be deposited today is P114,046.58 at 2.5% interest compounded monthly.

Answer 1

1) find the formula:

r=0.1

$Deferred Annuity = P(Ordinary) \times\frac{ (1 – (1 + r)^{-n})}{ ((1 + r)^t \times r)}$

$Deferred Annuity = 8000\times\frac{ (1 – (1 + 0.1)^{-12})}{ ((1 + 0.1)^5 \times0.1)}=33 846.13$

2)find the formula:

r=0.025

$Deferred Annuity = P(Ordinary) \times\frac{ (1 – (1 + r)^{-n})}{ ((1 + r)^t \times r)}$

$Deferred Annuity = 5000\times\frac{ (1 – (1 + 0.025)^{-32})}{ ((1 + 0.025)^8 \times0.025)}=89663.19$

3)find the formula:

r=0.1

$Deferred Annuity = P(Ordinary) \times\frac{ (1 – (1 + r)^{-n})}{ ((1 + r)^t \times r)}$

$Deferred Annuity = 13500\times\frac{ (1 – (1 + 0.1)^{-20})}{ ((1 + 0.1)^10 \times0.1)}=44311.69$

4)find the formula:

r=0.025

$Deferred Annuity = P(Ordinary) \times\frac{ (1 – (1 + r)^{-n})}{ ((1 + r)^t \times r)}$

$Deferred Annuity = 5000\times\frac{ (1 – (1 + 0.025)^{-24})}{ ((1 + 0.025)^12 \times0.025)}=66492.43$

$114 046.58-66492.43=47554.15$