Annuities

rad6210

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Sep 13, 2009
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Sara invests a total of $10,000. She uses part of the $10,000 to purchase an annuity with payments of $1,000 at the beginning of each year for 10 years. The purchase price of the annuity is its present value calculated at an annual effective interest rate of 8%. Sara invests the balance of her $10,000 in a 10-year certificate of deposit that earns nominal 9% per year compounded quarterly. As Sara receives payments from the annuity, she reinvests them at an annual effect interest rate of 7%. Calculate the annual effective yield rate on the entire $10,000 investment over the 10-year period.

The answer given is 7.95% and I need to show my work in terms like S-angle n and S-double-dot angle n, etc, which is new to me so any help would be great! thank you!
 
rad6210 said:
...in terms like S-angle n and S-double-dot angle n, etc, .....
Please clarify that. What do angles have to do with annuities?!
 
Oh sorry they're actuarial terms...
for example, "s angle n" = the accumulated value at the time of last payment = [(1+n)^n + 1]/i
and "s double-dot angle n" = the accumulated value one payment period after last payment

but any help just setting it up in regular numbers would be great too :)
 
rad6210 said:
Sara invests a total of $10,000. She uses part of the $10,000 to purchase an annuity with payments of $1,000 at the beginning of each year for 10 years. The purchase price of the annuity is its present value calculated at an annual effective interest rate of 8%. Sara invests the balance of her $10,000 in a 10-year certificate of deposit that earns nominal 9% per year compounded quarterly. As Sara receives payments from the annuity, she reinvests them at an annual effect interest rate of 7%. Calculate the annual effective yield rate on the entire $10,000 investment over the 10-year period.

PV of 10 annual payments of $1000 at 8% = a

10000 - a = b

FV of b invested at 9% per year cpd quarterly for 10 years = c

FV of 10 annual deposits of $1000 at annual rate of 7% = d

$10,000 has accumulated to $(c + d) after 10 years: what annual rate permits that?

Now show us what you can do :shock:
 
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