I need help answering the following question: This question is about math of fin

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I need help answering the following question:
This question is about math of finance
Please show steps
What amount must be deposited into an account which pays 4.3% interest compounded continuously in order of ake semiannual payments of $5,000 beginning a. six months from now? b. ten years from now?

The correct answer should be: A) $230,067.10 B) $152,913.29
I need help answering the following question:
This question is about math of finance
Please show steps
What amount must be deposited into an account which pays 4.3% interest compounded continuously in order of ake semiannual payments of $5,000 beginning a. six months from now? b. ten years from now?

The correct answer should be: A) $230,067.10 B) $152,913.29

This question is about math of finance
Please show steps
What amount must be deposited into an account which pays 4.3% interest compounded continuously in order of ake semiannual payments of $5,000 beginning a. six months from now? b. ten years from now?

The correct answer should be: A) $230,067.10 B) $152,913.29

Explanation / Answer

Let D be the deposit required. So, Present Value of the cash inflows and outflows must be zero

1

0=-D+5000e^(-0.043*0.5)+5000e^(-0.043*1)+5000e^(-0.043*1.5)+5000e^(-0.043*2)...........

=-D+5000e^(-0.043*0.5)/(1-e^(-0.043*0.5))

0=-D+230067.10

=>D=230067.10

2

0=-D+5000e^(-0.043*10)+5000e^(-0.043*10.5)+5000e^(-0.043*11)+5000e^(-0.043*11.5)...........

=-D+5000e^(-0.043*10)/(1-e^(-0.043*0.5))

0=-D+152913.29

=>D=152913.29

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