Question

1.Sasha owns two investments, A and B, that have a combined total value of 45,500 dollars. Investment A is expected to pay 20,500 dollars in 1 year(s) from today and has an expected return of 12.95 percent per year. Investment B is expected to pay 44,425 dollars in T years from today and has an expected return of 9.22 percent per year. What is T, the number of years from today that investment B is expected to pay 44,425 dollars? Round your answer to 2 decimal places (for example, 2.89, 14.70, or 6.00).

2.2 year(s) ago, Mack invested 6,570 dollars. In 2 year(s) from today, he expects to have 8,380 dollars. If Mack expects to earn the same annual return after 2 year(s) from today as the annual rate implied from the past and expected values given in the problem, then how much does Mack expect to have in 7 years from today?

3.3 year(s) ago, Xavier had 255,400 dollars in his account. In 6 year(s), he expects to have 411,900 dollars. If he has earned and expects to earn the same return each year from 3 year(s) ago to 6 year(s) from today, then how much does he expect to have in 2 year(s) from today?

4.

3 year(s) ago, Fatima invested 5,640 dollars. In 2 year(s) from today, she expects to have 7,720 dollars. If Fatima expects to earn the same annual return after 2 year(s) from today as the annual rate implied from the past and expected values given in the problem, then in how many years from today does she expect to have exactly 10,610 dollars? Round your answer to 2 decimal places (for example, 2.89, 14.70, or 6.00).

Answer 1

Sol 1: We have to first find the present value of Investment A: We will use the following formula for that: PV = FV/(1+Rate)^No of years; In case of Investment A we know that Future Value= $20,500.00 after No of Year= 1 and Rate = 12.95% thus substituting these values in the formula we would get Present Value of Investment A= $18,149.62.

Combined value of both investments are $45,500.00 as Investment A= $18,149.62 then Investment B= $45,500-$18,149.62 = $27,350.38

To calculate T for Investment B we have used NPER function of excel i.e.=NPER(rate,,pv,-fv,0) where Rate= 9.22%; Present Vale (PV)= $27,350.38 and FV = $44,425. Substituting the values in the Excel formula we will get 5.50 years. Thus T=5.50 years

Sol 2: Mack invested $ 6570 in the past and in Time 4 years (2yrs past + 2yrs future) the future Value: $ 8380. We would use the Rate function of Excel to find out the Annual Rate of Interest. The formula is =RATE (nper,,pv,-fv,0) here nper =4; PV= 6570 and FV= 8380, thus substituting the values in the formula we would get Rate= 6.27%

Now we would use the Rate of 6.27% to find the value of Mack Investment Amount today we could use Present Value formula i.e. PV= FV* (1/(1+rate)^nper) here FV= 8380; Rate = 6.27% and nper = 2 substituting the formula in the above formula we get the Present Value or Mack Investment value today = $7420.01

Finally to find the Mack investment amount 7 years from today will be found out by using the Future Value formula: PV* (1+rate)^nper; Here Present Value = 7420.01; Rate= 6.27%; nper= 7years substituting the values in Future Value formula we would get = $11,359.06

Sol 3: Xavier invested $2,55,400 in the past and in Time 9 years (3 yrs past + 6 yrs future) the future value: $4,11,900. We would use the Rate function of Excel to find out the Annual Rate of Interest. The formula is =RATE (nper,,pv,-fv,0) here nper= 9; PV= 255400 and FV=411900, thus substituting the values in the formula we would get Rate= 5.45%

Now we would use the Rate of 5.45% to find the value of Xavier Investment Amount today we will use Present Value formula i.e. PV= FV* (1/(1+rate)^nper) here FV= 411900; Rate = 5.45% and nper = 6 substituting the formula in the above formula we get the Present Value or Mack Investment value today = $2,99,509.91

Finally to find the Xavier investment amount 2 years from today will be found out by using the Future Value formula: PV* (1+rate)^nper; Here Present Value = 299509.91; Rate= 5.45%; nper= 2 years substituting the values in Future Value formula we would get = $3,33,071.95

Sol 4: Fatima invested $5640 in the past and in Time 5 years (3 yrs past + 2 yrs future) the future value: $7720. We would use the Rate function of Excel to find out the Annual Rate of Interest. The formula is =RATE (nper,,pv,-fv,0) here nper= 5; PV= 5640 and FV=7720, thus substituting the values in the formula we would get Rate= 6.48%

Now we would use the Rate of 6.48% to find the value of Fatima Investment Amount today we will use Present Value formula i.e. PV= FV* (1/(1+rate)^nper) here FV= 7720; Rate = 6.48% and nper = 2 substituting the formula in the above formula we get the Present Value or Mack Investment value today = $6808.98

Finally to find T for Investment of Fatima we have used NPER function of excel i.e.=NPER(rate,,pv,-fv,0) where Rate= 6.48%; Present Vale (PV)= $6808.98 and FV = $10,610. Substituting the values in the Excel formula we will get 7.06 years. Thus T=7.06 years