Description
Questions are attached below
Subject: Finance
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Explanation & Answer
Hi, Please check the attached file for detials, let me know if you have any questions, thank you. Best, James
Part Four
#2
What is the value today of a money machine that will pay $2,958.00 per year for 29.00 years?
Assume the first payment is made one year from today and the interest rate is 9.00%.
30166.52
Submit
#2:
29
1
(1 + 0.09)𝑛
𝑛=1
1
1
1.09 − (1.09)30
= 2958 ∗
1
1 − 1.09
2958
1
=
∗ (1 −
)
0.09
1.0929
= 30166.52
𝑃 = 2958.00 ∑
Answer format: Currency: Round to: 2 decimal places.
#3
What is the value today of a money machine that will pay $2,647.00 per year for 16.00 years?
Assume the first payment is made 4.00 years from today and the interest rate is 6.00%.
26750.30
Submit
Answer format: Currency: Round to: 2 decimal places.
#3
16
𝑃 = 2647.00 ∑
𝑛=1
1
(1 + 0.06)𝑛
1
1
−
1.06 (1.06)17
= 2647 ∗
1
1−
1.06
2647
1
=
∗ (1 −
)
0.06
1.0616
= 26750.30
#4
What is the value today of a money machine that will pay $2,161.00 every six months for 17.00
years? Assume the first payment is made six months from today and the interest rate is 12.00%.
31049.55
Submit
Answer format: Currency: Round to: 2 decimal places.
#4
6 months interest rate is 12%/2 =6% and the number of payments is 17*2 = 34, therefore, the present
value of the money machine is
34
𝑃 = 2161.00 ∑
𝑛=1
1
(1 + 0.06)𝑛
1
1
−
1.06 (1.06)35
= 2161 ∗
1
1 − 1.06
2161
1
=
∗ (1 −
)
0.06
1.0624
= 31049.55
What is the value today of a money machine that will pay $2,121.00 every six months for 22.00
years? Assume the first payment is made 5.00 years from today and the interest rate is 13.00%.
16601.88
#5.
6 months interest rate is 13%/2 =6.5% and the number of payments is 22*2 = 44, however the first
payment is 5 years from now, so we need to discount 1/(1+13%)5 to get the present value for today,
therefore, the present value of the money machine is
44
2121.00
1
𝑃=
∑
5
(1.13)
(1 + 0.065)𝑛
𝑛=1
1
1
−
1.065 (1.065)45
= 2121 ∗
1
1−
1.065
2121
1
=
∗ (1 −
)
5
0.065(1.13)
1.06544
= 16601.88
Part Five
#1
What is the value today of a money machine that will pay $5,819.00 per year for 24.00 years?
Assume the first payment is made today and that there are 24.0 total payments. The interest rate is
12.00%.
45297.00
Submit
Answer format: Currency: Round to: 2 decimal places.
23
𝑃 = 5819.00 ∑
𝑛=0
1
(1 + 0.12)𝑛
1
(1.12)24
1
1 − 1.12
1−
= 5819 ∗
5819
1
1.12 ∗ (1 −
)
0.12
1.1224
= 45297.00
=
#2
Derek will deposit $3,708.00 per year for 29.00 years into an account that earns 8.00%. The first
deposit is made next year. How much will be in the account 29.0 years from today?
385505.69
Submit
Answer format: Currency: Round to: 2 decimal places.
29
𝐹𝑉 = 3708.00 ∑(1 + 0.08)29−𝑛
𝑛=1
1
30
(1.08)
= 3808 ∗ (1.08)29
1
1−
1.08
3808
1
=
∗ 1.0829 ∗ (1 −
)
0.08
1.0829
= 385505.69
1−
#3
Derek will deposit $1,521.00 per year for 19.00 years into an account that earns 6.00%, The first
deposit is made next year. How much will be in the account 40.00 years from today?
51438.95
Submit
Answer format: Currency: Round to: 2 decimal places.
19
𝐹𝑉 = 1521.00 ∑(1 + 0.06)19−𝑛
𝑛=1
1
20
(1.06)
= 1521 ∗ (1.06)19
1
1 − 1.06
3808
1
=
∗ 1.0619 ∗ (1 −
)
0.06
1.0619
= 51438.95
1−
#4
Derek will deposit $2,610.00 per year for 19.00 years into an account that earns 12.00%. The first
deposit is made today. How much will be in the account 19.0 years from today? Note that he makes
19.0 total deposits.
185446.87
Submit
Answer format: Currency: Round to: 2 decimal places.
18
𝐹𝑉 = 2610.00 ∑(1 + 0.12)19−𝑛
𝑛=0
1
1
−
20
1.12
(1.12)
= 2610 ∗ (1.12)19
1
1 − 1.12
2610
1
=
∗ 1.1220 ∗ (1 −
)
0.12
1.1219
= 185446.87
#5
Derek will deposit $1,180.00 per year into an account starting today and ending in year 17.00. The
account that earns 9.00%. How much will be in the account 17.0 years from today?
47555.58
Submit
Answer format: Currency: Round to: 2 decimal places.
16
𝐹𝑉 = 1180.00 ∑(1 + 0.09)17−𝑛
𝑛=0
= 47555.58
#6
Derek has the opportunity to buy a money machine today. The money machine will pay Derek
$45,250.00 exactly 17.00 y...