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miskamm [114]
3 years ago
13

Sydney saved $10,000 during her first year of work after college and plans to invest it for her retirement in 40 years. how much

will she have available for retirement if she can make 8% on her investment?
Business
1 answer:
Yuliya22 [10]3 years ago
3 0
Given:
P = $10,000, the principal
t = 40 yers, time duration
r = 8% = 0.08, the interest rate
Assume that
n = 12, monthly compounding.

The value after 40 years is
A=P(1+ \frac{r}{n} )^{nt}
nt = 12*40 = 480
1 + r/n = 1 + 0.08/12 = 1.0066667
A = 10000*1.0066667⁴⁸⁰ = $242,737.71

Answer:  $242,737.71

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Calculate the following: The future value of lump-sum investment of $3,200 in four years that earns 6 percent. Round your answer
tresset_1 [31]

Answer:

(a) $4,040

(b) $3,434

(c) $348

(d) $3,265

Explanation:

(a) Calculate the following: The future value of lump-sum investment of $3,200 in four years that earns 6 percent. Round your answer to the nearest dollar. (Hint: Use Appendix A.1 or the Garman/Forgue companion website.) Round Future value of a Single Amount in intermediate calculations to four decimal places. $

To estimate this, the formula for calculating future value is used as follows:

FV = PV * (1 + r)^n ………………………….. (1)

Where,

FV = future value = ?

PV = lump-sum investment = $3,200

r = interest rate = 6%, or 0.06

n = number of years = 4

Substitute the values into equation (1) to have:

FV = $3,200 * (1 + 0.06)^4

FV = $3,200 * (1.06)^4

FV = $3,200 * 1.2625

FV = $4,040

(b) The future value of $1,100 saved each year for three years that earns 4 percent. Round your answer to the nearest dollar. (Hint: Use Appendix A.3 or the Garman/Forgue companion website.) Round Future value of Series of Equal Amounts in intermediate calculations to four decimal places. $

To calculate this, the formula for calculating the Future Value (FV) of an Ordinary Annuity is used as follows:

FV = M * (((1 + r)^n - 1) / r) ................................. (2)

Where,

FV = Future value of the amount after 3 years =?

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r = interest rate = 4%, or 0.04

n = number of years = 3

Substituting the values into equation (2), we have:

FV = $1,100 * (((1 + 0.04)^3 - 1) / 0.04)

FV = $1,100 * 3.1216

FV = $3,434

(c) A person who invests $1,800 each year finds one choice that is expected to pay 4 percent per year and another choice that may pay 7 percent. What is the difference in return if the investment is made for four years? Round your answer to the nearest dollar. (Hint: Use Appendix A.3 or the Garman/Forgue companion website.) Round Future value of Series of Equal Amounts in intermediate calculations to four decimal places. $

To do this, we first calculate the return of each of the 2  investments by using the the formula for calculating the Future Value (FV) of an Ordinary Annuity in part b above is used as follows:

<u>Calculation of return at 4 percent</u>

Where;

FV at 4% = Future value of the return after 4 years =?

M = Annual savings = $1,800

r = interest rate = 4%, or 0.04

n = number of years = 4

Substituting the values into equation (2), we have:

FV at 4% = $1,800 * (((1 + 0.04)^4 - 1) / 0.04)

FV  at 4% = $1,800 * 4.2465

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<u>Calculation of return at 7 percent</u>

Where;

FV at 7% = Future value of the return after 4 years =?

M = Annual savings = $1,800

r = interest rate = 7%, or 0.07

n = number of years = 4

Substituting the values into equation (2), we have:

FV at 7%= $1,800 * (((1 + 0.07)^4 - 1) / 0.07)

FV at 7% = $1,800 * 4.4399

FV at 7% = $7,992

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This is calculated as follows:

Difference = FV at 7% - FV at 4% = $7,992 - $7,644 = $348

(d) The amount a person would need to deposit today with a 7 percent interest rate to have $4,000 in three years. Round your answer to the nearest dollar. (Hint: Use Appendix A.2 or the Garman/Forgue companion website.) Round Present value of a Single Amount in intermediate calculations to four decimal places. $

To estimate this, the formula for calculating present value is used as follows:

PV = FV / (1 + r)^n ………………………….. (1)

Where;

PV = Present value or amount to deposit today = ?

FV = future value in three years = $4,000

r = interest rate = 7%, or 0.07

n = number of years = 3

Substitute the values into equation (1) to have:

PV = $4,000 / (1 + 0.07)^3

PV = $4,000 / 1.2250

PV = $3,265

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