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Lecture 25Annuities
Ana Nora Evans 403 [email protected]://people.virginia.edu/~ans5k
Math 1140 Financial Mathematics
2Math 1140 - Financial Mathematics
I think my grade on the quiz will be A) AB) BC) CD) DE) F
3Math 1140 - Financial Mathematics
Deferred Annuity
A deferred annuity is an annuity whose first payment is made two or more rent periods after the beginning of the term.
4Math 1140 - Financial Mathematics
Present Value
The present value a deferred annuity is located m periods before the present value of an ordinary annuity.To determine the present value of such a deferred annuity we need to move back m rent periods the present value of an ordinary annuity.
5Math 1140 - Financial Mathematics
Present Value
mn
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Math 1140 - Financial Mathematics6
On her eighteen birthday, Latisha receives an annuity that is to pay $5,000 on her 25th birthday through her 39th birthday. Calculate the value of the annuity on her 18th birthday using an annual effective interest rate of 5%.
Math 1140 - Financial Mathematics7
On her eighteen birthday, Latisha receives an annuity that is to pay $5,000 on her 25th birthday through her 39th birthday. Calculate the value of the annuity on her 18th birthday using an annual effective interest rate of 5%.
The correct answer is B.
A)
B)
C)
D)
615
)05.1(05.0
)05.1(1000,5$
715
)05.1(05.0
)05.1(1000,5$
616
)05.1(05.0
)05.1(1000,5$
716
)05.1(05.0
)05.1(1000,5$
8Math 1140 - Financial Mathematics
What about the maturity value of a deferred annuity?Do we need a new formula for that?
Math 1140 - Financial Mathematics9
10Math 1140 - Financial Mathematics
Forborne Annuity
A forborne annuity is an annuity whose last payment is made two or more rent periods before the end of the term.The maturity value is calculated p periods after the last payment.
11Math 1140 - Financial Mathematics
Future Value of a Forborne Annuity
The future value of a forborne annuity calculated p rent periods after the last payment is the future value of an ordinary annuity moved p rent periods forward.
12Math 1140 - Financial Mathematics
Future Value of a Forborne Annuity
pn
ii
iRS )1(
1)1(
Math 1140 - Financial Mathematics13
On her eighteen birthday, Latisha receives an annuity that is to pay $5,000 on her 25th birthday through her 39th birthday. Calculate the value of the annuity on her 50th birthday using an annual effective interest rate of 5%.
Math 1140 - Financial Mathematics14
On her eighteen birthday, Latisha receives an annuity that is to pay $5,000 on her 25th birthday through her 39th birthday. Calculate the value of the annuity on her 50th birthday using an annual effective interest rate of 5%.
A)
B)
C)
D)
1115
)05.1(05.0
1)05.1(000,5$
1215
)05.1(05.0
1)05.1(000,5$
1116
)05.1(05.0
1)05.1(000,5$
1216
)05.1(05.0
1)05.1(000,5$
Math 1140 - Financial Mathematics15
Math 1140 - Financial Mathematics16
On her eighteen birthday, Latisha receives an annuity that is to pay $5,000 on her 25th birthday through her 39th birthday. Calculate the value of the annuity on her 30th birthday using an annual effective interest rate of 5%.
The present value of the payments from the 31st birthday trough the 39th birthday on the 30th birthday is
The future value of the payments from the 25th birthday trough the 30th birthday on the 30th birthday is
05.0
)05.1(1000,5$
9
05.0
1)05.1(000,5$
6
Math 1140 - Financial Mathematics17
Monday
Read sections 5.5, 5.6
Exam 2
Wed, 2 Nov 2011, 7-9pm
Make-up
Thu, 3 Nov 2011, 7-9am
Charge
