Answer to Question #155346 in Financial Math for Bonevie tutor

Question #155346

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.


1
Expert's answer
2021-01-19T03:46:52-0500

1) find the formula:

r=0.1

"Deferred Annuity = P(Ordinary) \\times\\frac{ (1 \u2013 (1 + r)^{-n})}{ ((1 + r)^t \\times r)}"

"Deferred Annuity = 8000\\times\\frac{ (1 \u2013 (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 \u2013 (1 + r)^{-n})}{ ((1 + r)^t \\times r)}"

"Deferred Annuity = 5000\\times\\frac{ (1 \u2013 (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 \u2013 (1 + r)^{-n})}{ ((1 + r)^t \\times r)}"

"Deferred Annuity = 13500\\times\\frac{ (1 \u2013 (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 \u2013 (1 + r)^{-n})}{ ((1 + r)^t \\times r)}"

"Deferred Annuity = 5000\\times\\frac{ (1 \u2013 (1 + 0.025)^{-24})}{ ((1 + 0.025)^12 \\times0.025)}=66492.43"

"114 046.58-66492.43=47554.15"


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