1. Future Value -- If you deposit $10,000 in a bank account that pays 10 percent
ID: 1249851 • Letter: 1
Question
1. Future Value -- If you deposit $10,000 in a bank account that pays 10 percent interest annually, how much would be in your account after 5 years?
2. Present Value -- What is the present value of a security that will pay $5,000 in 20 years if securities of equal risk pay 7 percent annually?
3. Find the Required Interest Rate -- Your parents will retire in 18 years. They currently have $250,000 and they think they will need $1,000,000 at retirement. What annual interest rate must they earn to reach their goal, assuming they don’t save any additional funds?
4. If you invest $2,000 a year in a retirement account, how much would you have:
?a.?In 5 years at 6 percent?
?b.?In 20 years at 10 percent?
?c.?In 40 years at 12 percent?
5. What is the present value of:
?a.?$9,000 in 7 years at 8 percent?
?b.?$20,000 in 5 years at 10 percent?
?c.?$10,000 in 25 years at 6 percent?
Explanation / Answer
1. Future Value -- If you deposit $10,000 in a bank account that pays 10 percent interest annually, how much would be in your account after 5 years?
To find Future Value (F) given Present Value (P), we can use the factor tables at the end of the textbook or do a manual calculation.<?xml:namespace prefix = o ns = "urn:schemas-microsoft-com:office:office" />
F = P(1+i)n or F = P( F/P, i,n)
F = P( F/P, i,n)
= $10,000(F/P, 10, 5)
=$10,000 * 1.611
= $16,110
Thus, the future value is $16,110.
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2. Present Value -- What is the present value of a security that will pay $5,000 in 20 years if securities of equal risk pay 7 percent annually?
To find Present Value (P)given Future Value (F), we can use the factor tables at the end of the textbook or do a manual calculation.
P = F(1+i)%u2013n or P = F( P/F, i,n)
P = F( P/F, i,n)
= $5,000(P/F, 7, 20)
=$5,000 * 0.2584
= $1,292
Thus, the Present Value is $1,292.
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3. Find the Required Interest Rate -- Your parents will retire in 18 years. They currently have $250,000 and they think they will need $1,000,000 at retirement. What annual interest rate must they earn to reach their goal, assuming they don%u2019t save any additional funds?
Present value = $250,000
Future value = $1,000,000
N= 18 years and interest rate is calculated by the following expression.
F = P(1+i)n
(1+i)n = F/P
1+i = (F/P)%u2013n
i = (F/P)%u2013n %u20131
= ($1,000,000/ $250,000)%u201318 %u20131
= 4%u201318%u20131
= 1.08%u20131
= 0.08 or 8% in percent terms.
Thus, the interest rate is 8%
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4. If you invest $2,000 a year in a retirement account, how much would you have:
a) In 5 years at 6 percent?
F = P( F/P, i,n)
= $2,000(F/P, 6, 5)
=$2,000 * 1.338
= $2,676
Thus, the future value is $2,676.
b) In 20 years at 10 percent?
F = P( F/P, i,n)
= $2,000(F/P, 10, 20)
=$2,000 * 6.728
= $13,456
Thus, the future value is $13,456.
c.) In 40 years at 12 percent?
F = P( F/P, i,n)
= $2,000(F/P, 12, 40)
=$2,000 * 93.051
= $186,102
Thus, the future value is $186,102.
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5. What is the present value of:
a.)$9,000 in 7 years at 8 percent?
P = F( P/F, i,n)
P = F( P/F, i,n)
= $9,000(P/F, 8, 7)
=$9,000 * 0.5835
= $5,251.5
Thus, the Present Value is $5,251.5.
b) .$20,000 in 5 years at 10 percent?
P = F( P/F, i,n)
= $20,000(P/F, 10, 5)
=$20,000 * 0.6209
= $12,418
Thus, the Present Value is $12,418.
c.) $10,000 in 25 years at 6 percent?
P = F( P/F, i,n)
= $10,000(P/F, 6,25)
=$10,000 * 0.2330
= $2,330
Thus, the Present Value is $2,330.
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