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80. We are only concerned with the time it takes money to double, so the dollar amounts are irrelevant.
So, we can write the future value of a lump sum with continuously compounded interest as:
$2 = $1eRt
2 = eRt
Rt = ln(2)
Calculator Solutions
1.
Enter
10
7%
$4,800
N
I/Y
PV
PMT
FV
$9,442.33
$9,442.33 – 8,160 = $1,282.33
2.
Enter
10
6%
$3,550
N
I/Y
PV
PMT
FV
Solve for
$6,357.51
Enter
10
8%
$3,550
N
I/Y
PV
PMT
FV
Solve for
$7,664.18
Enter
20
6%
$3,550
N
I/Y
PV
PMT
FV
Solve for
$11,385.33
3.
Enter
9
7%
$15,451
N
I/Y
PV
PMT
FV
Solve for
$8,404.32
Solve for
$108,890.97
Enter
24
11%
$550,164
N
I/Y
PV
PMT
FV
Solve for
$44,951.14
4.
Enter
3
$217
$293
N
I/Y
PV
PMT
FV
Solve for
10.53%
Enter
10
$432
$1,053
N
I/Y
PV
PMT
FV
Solve for
9.32%
Enter
16
$41,000
$162,181
N
I/Y
PV
PMT
FV
Solve for
8.97%
Enter
19
$54,382
$483,500
N
I/Y
PV
PMT
FV
Solve for
12.19%
5.
Enter
6%
$625
$1,284
N
I/Y
PV
PMT
FV
Solve for
12.36
Enter
9%
$810
$4,341
N
I/Y
PV
PMT
FV
Solve for
19.48
Enter
7%
$18,400
$234,162
N
I/Y
PV
PMT
FV
Solve for
37.60
Enter
10%
$21,500
$215,000
N
I/Y
PV
PMT
FV
Solve for
24.16
6.
Enter
5.75%
$1
$2
N
I/Y
PV
PMT
FV
Solve for
12.40
Enter
5.75%
$1
$4
N
I/Y
PV
PMT
FV
Solve for
24.80
7.
Enter
20
5.6%
$540,000,000
N
I/Y
PV
PMT
FV
Solve for
$181,599,812.54
8.
Enter
3
$1,680,000
$1,100,000
N
I/Y
PV
PMT
FV
Solve for
–13.17%
11.
CFo
$0
CFo
$0
CFo
$0
C01
$585
C01
$585
C01
$585
F01
1
F01
1
F01
1
C02
$815
C02
$815
C02
$815
F02
1
F02
1
F02
1
C03
$1,630
C03
$1,630
C03
$1,630
F03
1
F03
1
F03
1
C04
$2,140
C04
$2,140
C04
$2,140
F04
1
F04
1
F04
1
I = 5
I = 13
I = 18
NPV CPT
NPV CPT
NPV CPT
$4,465.01
$3,598.14
$3,176.94
12.
Enter
9
5%
$4,850
N
I/Y
PV
PMT
FV
Solve for
$34,472.94
Enter
5
5%
$6,775
N
I/Y
PV
PMT
FV
Solve for
$29,332.20
Enter
9
21%
$4,850
N
I/Y
PV
PMT
FV
Solve for
$18,941.36
Enter
5
21%
$6,775
N
I/Y
PV
PMT
FV
Solve for
$19,823.54
13.
Enter
15
7.5%
$5,500
N
I/Y
PV
PMT
FV
Solve for
$48,549.16
Enter
40
7.5%
$5,500
N
I/Y
PV
PMT
FV
Solve for
$69,269.25
Enter
75
7.5%
$5,500
N
I/Y
PV
PMT
FV
Solve for
$73,009.99
15.
Enter
9.8%
4
NOM
EFF
C/Y
Solve for
10.17%
Enter
12.4%
12
NOM
EFF
C/Y
Solve for
13.13%
Enter
7.6%
365
NOM
EFF
C/Y
Solve for
7.90%
16.
Enter
10.4%
2
NOM
EFF
C/Y
Solve for
10.14%
Enter
8.9%
12
NOM
EFF
C/Y
Solve for
8.56%
Enter
11.6%
52
NOM
EFF
C/Y
Solve for
10.99%
17.
Enter
15.7%
12
NOM
EFF
C/Y
Solve for
16.88%
Enter
16.2%
2
NOM
EFF
C/Y
Solve for
16.86%
18. 2nd BGN 2nd SET
Enter
12
$108
$10
N
I/Y
PV
PMT
FV
Solve for
1.98%
Enter
102.77%
52
NOM
EFF
C/Y
Solve for
176.68%
19.
Enter
1.3%
$18,700
$450
N
I/Y
PV
PMT
FV
Solve for
60.16
20.
Enter
1,733.33%
52
NOM
EFF
C/Y
Solve for
313,916,515.69%
21.
Enter
6
7.2%
$1,500
N
I/Y
PV
PMT
FV
Solve for
$2,276.46
Enter
6 × 2
7.2%/2
$1,500
N
I/Y
PV
PMT
FV
Solve for
$2,293.02
Enter
6 × 12
7.2%/12
$1,500
N
I/Y
PV
PMT
FV
Solve for
$2,307.52
23. Stock account:
Enter
360
10.5%/12
$750
N
I/Y
PV
PMT
FV
Solve for
$1,887,300.74
Bond account:
Enter
360
6.1%/12
$325
N
I/Y
PV
PMT
FV
Solve for
$332,782.27
Savings at retirement = $1,887,300.74 + 332,782.27 = $2,220,083.01
Enter
300
6.9%/12
$2,220,083.01
N
I/Y
PV
PMT
FV
Solve for
$15,549.74
24.
Enter
12/3
$1
$3
N
I/Y
PV
PMT
FV
Solve for
31.61%
25.
Enter
5
$55,000
$105,000
N
I/Y
PV
PMT
FV
Solve for
13.81%
Enter
11
55,000
$235,000
N
I/Y
PV
PMT
FV
Solve for
14.11%
28.
Enter
23
6.8%
$5,700
N
I/Y
PV
PMT
FV
Solve for
$65,363.72
Enter
2
6.8%
$65,363.72
N
I/Y
PV
PMT
FV
Solve for
$57,305.23
29.
Enter
15
12%
$825
N
I/Y
PV
PMT
FV
Solve for
$5,618.96
Enter
5
9%
$5,618.96
N
I/Y
PV
PMT
FV
Solve for
$3,651.94
30.
Enter
30 × 12
5.4%/12
.80($825,000)
N
I/Y
PV
PMT
FV
Solve for
$3,706.10
Enter
22 × 12
5.4%/12
$3,706.10
N
I/Y
PV
PMT
FV
Solve for
$571,856.86
31.
Enter
6
1.9%/12
$7,500
N
I/Y
PV
PMT
FV
Solve for
$7,571.53
Enter
6
16%/12
$7,571.53
N
I/Y
PV
PMT
FV
Solve for
$8,197.81
$8,197.81 – 7,500 = $697.81
35.
Enter
15
10%
$5,250
N
I/Y
PV
PMT
FV
Solve for
$39,931.92
Enter
15
5%
$5,250
N
I/Y
PV
PMT
FV
Solve for
$54,493.20
Enter
15
15%
$5,250
N
I/Y
PV
PMT
FV
Solve for
$30,698.69
36.
Enter
8.75%/12
$190
$25,000
N
I/Y
PV
PMT
FV
Solve for
92.59
37.
Enter
60
$105,000
$2,025
N
I/Y
PV
PMT
FV
Solve for
.492%
38.
Enter
360
5.1%/12
$875
N
I/Y
PV
PMT
FV
Solve for
$161,156.71
Enter
360
5.1%/12
$63,843.29
N
I/Y
PV
PMT
FV
Solve for
$293,885.25
39.
CFo
$0
C01
$1,300
F01
1
C02
$0
F02
1
C03
$1,900
F03
1
C04
$2,450
F04
1
I = 8%
NPV CPT
$4,512.81
Enter
2
8%
$1,287.19
N
I/Y
PV
PMT
FV
Solve for
$1,501.38
40.
CFo
$1,000,000
C01
$1,165,000
F01
1
C02
$1,330,000
F02
1
C03
$1,495,000
F03
1
C04
$1,660,000
F04
1
C05
$1,825,000
F05
1
C06
$1,990,000
F06
1
C07
$2,155,000
F07
1
C08
$2,320,000
F08
1
C09
$2,485,000
F09
1
C010
$2,650,000
I = 7.5%
NPV CPT
$13,423,365.99
41.
Enter
360
.80($3,900,000)
$18,250
N
I/Y
PV
PMT
FV
Solve for
.481%
Enter
5.77%
12
NOM
EFF
C/Y
Solve for
5.93%
42.
Enter
3
11%
$150,000
N
I/Y
PV
PMT
FV
Solve for
$109,678.71
Enter
3
$102,000
$150,000
N
I/Y
PV
PMT
FV
Solve for
13.72%
43.
Enter
24
7.6%
$3,500
N
I/Y
PV
PMT
FV
Solve for
$38,113.74
Enter
6
7.6%
$38,113.74
N
I/Y
PV
PMT
FV
Solve for
$24,558.84
44.
Enter
96
8.6%/12
$1,750
N
I/Y
PV
PMT
FV
Solve for
$121,161.48
Enter
84
11.4%/12
$1,750
$121,161.48
N
I/Y
PV
PMT
FV
Solve for
$155,716.71
45.
Enter
15 × 12
6.15%/12
$1,250
N
I/Y
PV
PMT
FV
Solve for
$368,207.73
46. PV@ T = 14: $3,250/.064 = $50,781.25
Enter
7
6.4%
$50,781.25
N
I/Y
PV
PMT
FV
Solve for
$32,893.64
47.
Enter
12
$23,000
$2,234.83
N
I/Y
PV
PMT
FV
Solve for
2.446%
Enter
29.35%
12
NOM
EFF
C/Y
Solve for
33.64%
48. Monthly rate = .09/12 = .0075; semiannual rate = (1.0075)6 – 1 = 4.59%
Enter
10
4.59%
$6,500
N
I/Y
PV
PMT
FV
Solve for
$51,217.83
Enter
8
4.59%
$51,217.83
N
I/Y
PV
PMT
FV
Solve for
$35,781.50
Enter
12
4.59%
$51,217.83
N
I/Y
PV
PMT
FV
Solve for
$29,907.30
Enter
18
4.59%
$51,217.83
N
I/Y
PV
PMT
FV
Solve for
$22,853.63
