Answered

Westonci.ca offers quick and accurate answers to your questions. Join our community and get the insights you need today. Join our Q&A platform to connect with experts dedicated to providing precise answers to your questions in different areas. Join our Q&A platform to connect with experts dedicated to providing accurate answers to your questions in various fields.

John invests a total of 10,000. He purchases an annuity with payments of 1,000 at the beginning of each year for 10 years at an effective annual interest rate of 8%. As annuity payments are received, they are reinvested at an effective annual interest rate of 7%. The remaining balance of the 10,000 is invested in a 10-year certificates of deposit with a nominal annual interest rate of 9%, compounded quarterly. Calculate the annual effective yield rate on the entire 10,000 investment over the 10-year period.

Sagot :

Answer:

7.95%

Explanation:

the first step is to determine the present value of the 10 year annuity

[tex]1000\frac{(1 + 0.08)(1 - (1 - 0.08)^{-10} }{0.08}[/tex] = 7246.89

remaining balance of the 10,000 is invested in a 10-year certificates of deposit = 10,000 - 7246.89 =  $2753.11

We would calculate the future value of this amount

The formula for calculating future value:

FV = P (1 + r/m)^mn

FV = Future value  

P = Present value  

R = interest rate  

N = number of years  

m = number of compounding

$2753.11 x ( 1 + 0.09/4)^(4 x 10) = 6704.34

calculate the value of reinvestments

[tex]1000\frac{(1 + 0.07) ( 1 + 0.07)^{10} - 1 }{0.07}[/tex] = 14783.60

14783.60 + 6704.34 = 10,000 ( 1 + er)^10

er = 0.0795 = 7.95%

Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. Thank you for choosing Westonci.ca as your information source. We look forward to your next visit.