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Question No. 6: Toni decides to establish an endowment fund to benefit one Bcum Project Finance student at UNY each year. She would like the fund to pay a qualified student each year a one-time grant of US$1,200. However, this annual on-off grant to each student is growing at the rate of 4% to account for inflation. She estimates that the fund could earn an interest rate of 7% per annum. How much should Tony deposit in the fund today?

Question No. 7: What is the future value of $12,000 for 4.5 years continuously compounding at 10.5%?

Step 1

Question No. 6: To calculate the amount Toni should deposit in the fund today, we need to use the present value formula: PV=FV(1+r)n
Where: PV is the present value of the future grant payments

FV is the future value of the grant payments after n years

r is the interest rate per yearn is the number of years In this case, we want to find the amount Toni should deposit today to provide a one-time grant of US$1,200 per year, adjusted for inflation at a rate of 4% per year, to one student at UNY each year. Assuming that the grant payments will continue indefinitely, we can use the perpetuity formula to calculate the future value:
FV=PMTr
Where: PMT is the annual paymentr is the interest rate per year Substituting the given values: PMT = US$1,200
Endowment Fund to Benefit One Bcum Project Finance Student at UNY Essay
r = 7% per annum

n = indefinitely
FV=US$1,2000.07=US$17,142.86

Now we can calculate the present value of this future value using the present value formula, assuming that the grant payments will continue indefinitely:

PV=US$17,142.86(1+0.04)n

We can simplify this formula by assuming that the grant payments will continue forever, and use the perpetuity formula instead:
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PV=PMTr−g
Where: g is the growth rate of the grant payments (inflation rate) Substituting the given values: PMT = US$1,200

r = 7% per annum PV=US$1,2000.07−0.04=US$40,000

Explanationfor step 1

Therefore, Toni should deposit US$40,000 in the fund today to provide a one-time grant of US$1,200 per year, adjusted for inflation at a rate of 4% per year, to one student at UNY each year.
Step 2

Question No. 7: To calculate the future value of $12,000 for 4.5 years continuously compounding at 10.5%, we can use the formula for continuous compounding: FV=PV×er×t

Where: PV is the present value (in this case, $12,000)r is the annual interest rate (in decimal form, 0.105)t is the time period (in this case, 4.5 years) Substituting the given values: FV=$12,000×e0.105×4.5=$19,786.26

So final answer is next step

Final answer

Therefore, the future value of $12,000 for 4.5 years continuously compounding at 10.5% is $19,786.26. Endowment Fund to Benefit One Bcum Project Finance Student at UNY Essay

Expert Answer

Question No. 6: Toni decides to establish an endowment fund to benefit one Bcum Project Finance student at UNY each year. She would like the fund to pay a qualified student each year a one-time grant of US$1,200. However, this annual on-off grant to each student is growing at the rate of 4% to account for inflation. She estimates that the fund could earn an interest rate of 7% per annum. How much should Tony deposit in the fund today? Question No. 7: What is the future value of $12,000 for 4.5 years continuously compounding at 10.5%? Step 1

Question No. 6: To calculate the amount Toni should deposit in the fund today, we need to use the present value formula: PV=FV(1+r)n

Where: PV is the present value of the future grant payments

FV is the future value of the grant payments after n years

r is the interest rate per yearn is the number of years In this case, we want to find the amount Toni should deposit today to provide a one-time grant of US$1,200 per year, adjusted for inflation at a rate of 4% per year, to one student at UNY each year. Assuming that the grant payments will continue indefinitely, we can use the perpetuity formula to calculate the future value:

FV=PMTr

Where: PMT is the annual paymentr is the interest rate per year Substituting the given values: PMT = US$1,200

Endowment Fund to Benefit One Bcum Project Finance Student at UNY Essay

r = 7% per annum

n = indefinitely

FV=US$1,2000.07=US$17,142.86

Now we can calculate the present value of this future value using the present value formula, assuming that the grant payments will continue indefinitely:

PV=US$17,142.86(1+0.04)n

We can simplify this formula by assuming that the grant payments will continue forever, and use the perpetuity formula instead:

ORDER A PLAGIARISM-FREE PAPER HERE

PV=PMTr−g

Where: g is the growth rate of the grant payments (inflation rate) Substituting the given values: PMT = US$1,200

r = 7% per annum PV=US$1,2000.07−0.04=US$40,000

Explanationfor step 1

Therefore, Toni should deposit US$40,000 in the fund today to provide a one-time grant of US$1,200 per year, adjusted for inflation at a rate of 4% per year, to one student at UNY each year.

Step 2

Question No. 7: To calculate the future value of $12,000 for 4.5 years continuously compounding at 10.5%, we can use the formula for continuous compounding: FV=PV×er×t

Where: PV is the present value (in this case, $12,000)r is the annual interest rate (in decimal form, 0.105)t is the time period (in this case, 4.5 years) Substituting the given values: FV=$12,000×e0.105×4.5=$19,786.26

So final answer is next step

Final answer

Therefore, the future value of $12,000 for 4.5 years continuously compounding at 10.5% is $19,786.26. Endowment Fund to Benefit One Bcum Project Finance Student at UNY Essay

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