Question 1205437
she needs 57,500,000 at the end of 2029.
the initial investment is at the beginning of the year 2023.
the interest rate is 9% compounded semi-annually.


the semi-annual interest rate is 9% divided by 2 = 4.5% every 6 months.


2029 minus 2023 = 6 years.


you can use the calculator at <a href = "https://arachnoid.com/finance/" target = "_blank">https://arachnoid.com/finance/</a> to solve these problems.


1: What single payment could be made at the beginning of the year 2023 to achieve this objective?


future value = 57,500,000
interest rate per semi-annual time period = 4.5%
number of time periods = 6 years * 2 semi-annual time periods per year = 12 semi-annual time periods.
payments per semi-annual time period = 0
payments made at the end of each semi-annual time period is not used.


calculator tells you that the present value needs to be 33,905,672.23.


here's what it looks like on the calculator.


<img src = "http://theo.x10hosting.com/2023/122012.jpg">


2: What amount could Lady Lee invest at the end of each year annually up to the year 2029 to achieve this same objective?


use the same calculator.


present value = 0
future value = 57,500,000
interest rate per annual time period = 9% per annual time period divided by 2 = 4.5% per semi-annual time period.
that is divided by 100 to get .045 and then has 1 added to it to get 1.045 and then raised to the power of 2 to get 1.045^2 = 1.092025 and then has 1 subtracted from it to get .092025 multiplied by 100 = 9.2025% per annual time period.
number of annual time periods = 6.
payments are made at the end of each annual time period.


calculator tells you that the payments made at the end of each annual time period = 7,603,935.46.


since the interest rate is compounded semi-annually, the nominal interest rate of 9.0 is divided by 2 to get a semi-annual interest rate of 4.5%.
that is then divided by 100 to get .045 and added to 1 to get 1.045 and raised to the power of 2 to get 1.045^2 = 1.092025.
it then has 1 subtracted from it to bet .092025 and is then multiplied by 100 to get 9.2025%.
that's the interest rate per annual time period used in the calculator for problem number 2.


here's what it looks like in the calculator.



<img src = "http://theo.x10hosting.com/2023/122011.jpg">


le me know if you have any questions.


theo