Finding the interest rate and the number of years okmarks People Window Help y A

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Finding the interest rate and the number of years okmarks People Window Help y Aplia: Student Question × (?MindTap-Cengage Learning courses.aplia.com/af/servlet/quiz?quiz action takeQuiz&quiz; probGuid-QNAPCOA8010100000041ca25e00a000 Time Value of Money Graded Assignment Read Chapter 5 | Back to Assignment Due Sunday 06.17.18 at 11:45 P Keep the Highest:/3 Attempts 7. Finding the interest rate and the number of years The future value and present value equations also help in finding the interest rate and the number of years that correspond to present and future value calculations. If a security currently worth $2,0 will be worth $2,433.31 five years in the future, what is the implied interest rate the investor will earn on the security-assuming that no additional deposits or withdrawals are made? ? 4.00% ? 8.22% o 1.22% 3.20% If an investment of $50,000 is earning an interest rate of 4.00%, compounded annually, then it will take for this investment to reach a value of $71,165.59-assuming that no additional deposits or withdrawals are made during this time. ments is true-assuming that no addtional deposits or withdrawals are made? Which of the following is true-assuming that no additional deposits or withdrawals are made? O If you invest si today at 15% annual compound interest for 82.3753 years, youn end up with S100.000. Q If you invest $5 today at 15% annual compound interest for 82.3753 years, you'll end up with $100,000.

Explanation / Answer

Answer a.

Present Value = $2,000
Future Value = $2,433.31
Annual Interest Rate = i%
Period = 5 years

Present Value * (1 + Interest Rate)^Period = Future Value
$2,000 * (1 + i)^5 = $2,433.31
(1 + i)^5 = 1.2167
1 + i = 1.0400
i = 0.04
i = 4.00%

So, interest rate earned is 4.00%

Answer b.

Present Value = $2,000
Future Value = $2,433.31
Annual Interest Rate = 4%
Period = n years

Present Value * (1 + Interest Rate)^Period = Future Value
$50,000 * (1 + 0.04)^n = $71,165.59
1.04^n = 1.42331
n * ln(1.04) = ln(1.42331)
n = 9.00

So, period is 9 years

Answer c.

TRUE: If you invest $1 today at 15% annual compound interest for 82.3753 years, you’ll end with $100,000

Present Value = $1
Annual Interest Rate = 15%
Period = 82.3753 years

Future Value = Present Value * (1 + Interest Rate)^Period
Future Value = $1 * 1.15^82.3753
Future Value = $100,000

FALSE: If you invest $5 today at 15% annual compound interest for 82.3753 years, you’ll end with $100,000

Present Value = $5
Annual Interest Rate = 15%
Period = 82.3753 years

Future Value = Present Value * (1 + Interest Rate)^Period
Future Value = $5 * 1.15^82.3753
Future Value = $500,000

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