Question

Sasha owns two investments, A and B, that have a combined total value of 44,700 dollars. Investment A is expected to pay 26,600 dollars in 7 year(s) from today and has an expected return of 4.81 percent per year. Investment B is expected to pay 32,950 in 2 years from today and has an expected return of R per year. What is R, the expected annual return for investment B? Answer as a rate in decimal format so that 12.34% would be entered as .1234 and 0.98% would be entered as .0098.

Sasha owns two investments, A and B, that have a combined total value of 41,000 dollars. Investment A is expected to pay 26,400 dollars in 1 year(s) from today and has an expected return of 17.88 percent per year. Investment B is expected to pay 42,479 dollars in T years from today and has an expected return of 7.7 percent per year. What is T, the number of years from today that investment B is expected to pay 42,479 dollars? Round your answer to 2 decimal places (for example, 2.89, 14.70, or 6.00).

Answer 1

Answer to Question 1:

Investment A:

Future Value = $26,600
Time Period = 7 years
Interest Rate = 4.81%

Present Value of Investment A = Future Value / (1 + Interest Rate)^Time Period
Present Value of Investment A = $26,600 / 1.0481^7
Present Value of Investment A = $19,145.31824

Investment B:

Present Value of Investment B = Total Investment - Present Value of Investment A
Present Value of Investment B = $44,700 - $19,145.31824
Present Value of Investment B = $25,554.68176

Future Value = $32,950
Time Period = 2 years

Present Value of Investment B = Future Value / (1 + Interest Rate)^Time Period
$25,554.68176 = $32,950 / (1 + Interest Rate)^2
(1 + Interest Rate)^2 = 1.289392
1 + Interest Rate = 1.1355
Interest Rate = 0.1355 or 13.55%

Answer to Question 2:

Investment A:

Future Value = $26,400
Time Period = 1 year
Interest Rate = 17.88%

Present Value of Investment A = Future Value / (1 + Interest Rate)^Time Period
Present Value of Investment A = $26,400 / 1.1788^1
Present Value of Investment A = $22,395.6566

Investment B:

Present Value of Investment B = Total Investment - Present Value of Investment A
Present Value of Investment B = $41,000 - $22,395.6566
Present Value of Investment B = $18,604.3434

Future Value = $42,479
Interest Rate = 7.70%

Present Value of Investment B = Future Value / (1 + Interest Rate)^Time Period
$18,604.3434 = $42,479 / 1.0770^Time Period
1.0770^Time Period = 2.283284
Time Period * ln(1.0770) = ln(2.283284)
Time Period = 11.13 years