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1) You have an opportunity to invest $500 in an investment fund that pays 7
1) You have an opportunity to invest $500 in an investment fund that pays 7.5% annual interest. How much money will the investment fund have after 8 years?
2) An investment fund has $10,000 and yields 6% interest annually. How many years will it take for the fund to grow by five times?
3) What is the present value of a $1,000 fund that has a 4% interest rate over 9 years?
4) You are a millionaire and you wish endow a children's foundation with sufficient money to fund ongoing scholarships. The Children's Scholarship Fund of Charlotte (CFC) asked you to partner with them and start up a scholarship fund with $500,000 disbursements. The fund will grow by 2% in perpetuity annually at an interest rate of 4%. How much do you need to initially invest into the CFC?
5) Jim and Mary Cummings just had their first child, and they want to begin saving for college expenses. They estimate they will need a college fund worth $100,000 to pay for four years of college costs. They plan to set aside $2,700 at the end of each year for the next 18 years, at an investment interest rate of 8% interest. Given that plan, how long will it take Jim and Mary to accumulate the money they need?
Expert Solution
1) Computation of the future value:-
FV = PV*(1+rate)^n
= $500*(1+7.5%)^8
= $500*1.78348
= $891.74
2) We can calculate the number of years by using the following formula in excel:-
=nper(rate,pmt,-pv,fv)
Here,
Nper = Number of years
Rate = 6%
Pmt = 0
PV = $10,000
FV = $10,000*5 = $50,000
Substituting the values in formula:
= nper(6%,0,-10000,50000)
= 27.62 years
3) Computation of the present value:-
FV = PV*(1+rate)^n
$1,000 = PV*(1+4%)^9
PV = $1,000/1.42331
= $702.59
4) Computation of the funds need to initially invest into the CFC:-
Needed fund = Annual disbursements / (Annual return - Growth rate)
= $500,000 / (4% - 2%)
= $500,000 / 2%
= $25,000,000
5) We can calculate the number of years by using the following formula in excel:-
=nper(rate,pmt,pv,-fv)
Here,
Nper = Number of years
Rate = 8%
Pmt = $2,700
PV = 0
FV = $100,000
Substituting the values in formula:
= nper(8%,2700,0,-100000)
= 17.89 years
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