Question

Asked Mar 31, 2019

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Step 1

Calculating the implied interest rate the investor will earn on the security by using the formula of future value of money. We have,

Future value of money = C_{0 }(1+r)^{n }

Here,

C_{0 }= Cash flow at period 0 = $ 9,200

Future value of money = $ 12,106.57

r = Rate of interest =?

n = Number of periods = 7 years

By substituting these value in the above formula. We get,

$ 12,106.57 = $ 9,200 (1+ r)^{7 }

(1+r)^{7 }= $ 12,106.57 / $ 9,200

(1 +r)^{7 }= 1.31593152173

(1+r) = (1.31593152173)^{1/7 }

(1+r) = 1.0400

r = 1.0400 – 1

r = 0.0400*100

r = 4.00 %

Therefore, the implied rate of interest the investor will earn on the security shall be 4.00%.

Step 2

Calculating the number of periods in which the investor will earn on the security by using the formula of future value of money. We have,

Future value of money = C_{0 }(1+r)^{n }

Here,

C_{0 }= Cash flow at period 0 = $ 35,000

Future value of money = $ 41,755.92

r = Rate of interest =4.00 %

n = Number of periods =?

By substituting these value in the above formula. We get,

$ 41,755.92 = $ 35,000 (1.04)^{n }

(1.04)^{n }= $ 41,755.92 / $ 35,000

(1.04)^{n }= 1.19302628571

(1.04)^{n }= (1.04)^{4.5 }

n = 4.5 years

Therefore, the number of periods in which the investor will earn on the security shall be 4.5 years.

Step 3

Calculating the future value of money. We have,

Future value of money = C0 (1+r)n

Here,

C0 = Cash flow at period 0 = $ 500

Future value of money =?

r = Rate of interest =5.00 %

n = Number of periods = 10.50 years

By substituting these value in the above f...

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