12-1 Compound Interest. 12-2 Compound Interest and Present Value.
Compound Interest Problems. Lesson Objectives Use the compound interest formula to solve problems...
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Transcript of Compound Interest Problems. Lesson Objectives Use the compound interest formula to solve problems...
![Page 1: Compound Interest Problems. Lesson Objectives Use the compound interest formula to solve problems Use the compound interest formula to solve problems.](https://reader031.fdocuments.net/reader031/viewer/2022032006/56649eea5503460f94bfb54e/html5/thumbnails/1.jpg)
Compound Interest Compound Interest ProblemsProblems
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Lesson ObjectivesLesson Objectives
Use the compound interest formula to Use the compound interest formula to solve problemssolve problems
Simple interest Simple interest I = P*r*tI = P*r*tCompound interest Compound interest
Continuously compounded interestContinuously compounded interestA = PeA = Pertrt
nt
n
rPA
1
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Vocabulary
simple interestprincipalrate of interestcompound interest
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The formulas…The formulas…
n = # times compounded / n = # times compounded / yearyear
r = rater = rate
t = time (in years)t = time (in years)
P= principal(initial \) amt.P= principal(initial \) amt.
Continuously compounded Continuously compounded interestinterest A = PeA = Pertrt
Simple interestSimple interest I= I= (P*r*t)(P*r*t)
Compound interestCompound interest
nt
n
rPA
1
n
n ne
e
11lim
...718281827.2
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The table shows some common compounding periods and how many times per year interest is paid for them.
Compounding Periods Times per year (n)
Annually 1
Semi-annually 2
Quarterly 4
Monthly 12
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Example 1-2Example 1-2Suppose $10,000 is invested at 5.4%, Suppose $10,000 is invested at 5.4%,
compounded compounded monthly.monthly.
a) What is the balance after 2 yrs? 5 yrs?a) What is the balance after 2 yrs? 5 yrs?
2*12
12
054.01000,10
A
5*12
12
054.01000,10
A
240045.1000,10
78.137,11$
600045.1000,10
71.091,13$
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David invested $1800 in a savings account that pays 4.5% interest compounded semi-annually. Find the value of the investment in 12 years.
Example 3: You Try!
Use the compound interest formula.
Substitute.
= 1800(1 + 0.0225)24 Simplify.
A = P(1 + )r n
nt
= 1800(1 + )0.045 t 2
2(12)
= 1800(1.0225)24 Add inside the parentheses.
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#3 Continued
After 12 years, the investment will be worth about $3,070.38.
≈ 1800(1.70576) Find (1.0225)24 and round.
≈ 3,070.38 Multiply and round to the nearest cent.
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Example 4-5Example 4-5
Suppose $5,000 is invested at 6%, compounded Suppose $5,000 is invested at 6%, compounded continuously.continuously.
a) What is the balance after 2 yrs? a) What is the balance after 2 yrs? You try: 5 yrsYou try: 5 yrs??
2*06.0000,5 eA 5*06.0000,5 eA
1275.1000,5
48.637,5$
34986.1000,5
29.749,6$
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Example 6Example 6I have I have $2,500$2,500 to invest and need to invest and need $4,000$4,000 in in 6 6
yearsyears. I found an account that pays 8% interest . I found an account that pays 8% interest (compounded daily)(compounded daily)
A) At this rate, will I get my money?A) At this rate, will I get my money?
6*365
365
08.01500,2
A
2190000219.1500,2
97.039,4$
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Kia invested $3700 in a savings account that pays 2.5% interest compounded quarterly. Find the value of the investment in 10 years.
Guided Practice. Example 7 – YOU TRY!
Use the compound interest formula.
Substitute.
= 3700(1 + 0.00625)40 Simplify.
A = P(1 + )r n
nt
= 3700(1 + )0.025 t 4
4(10)
= 3700(1.00625)40 Add inside the parentheses.
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Check It Out! Example 7 Continued
After 10 years, the investment will be worth about $4,747.20.
≈ 3700(1.28303) Find (1.00625)40 and round.
≈ 4,747.20 Multiply and round to the nearest cent.
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4 CORNERS : Part I
Theresa invested $800 in a savings account that pays
4% interest compounded quarterly. Find the value of the investment after 6 years.A. $1156. 79
B. $1015.79
C. $1014.39
D. $1015.85
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STOP! Hw STOP! Hw
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Ex.8Ex.8
Suppose $10,000 is invested at 5.4%, Suppose $10,000 is invested at 5.4%, compounded monthlycompounded monthly. . Using Log/Ln to find “t”. Using Log/Ln to find “t”.
b) What is the doubling time?b) What is the doubling time?
yearsn 86.120045.1ln12
2ln
n*12
12
054.01000,10000,20
n120045.12
0045.1ln122ln n
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Ex.9 Suppose $5,000 is invested at 6%, Ex.9 Suppose $5,000 is invested at 6%, compounded continuously.compounded continuously.
b) What is the doubling time?b) What is the doubling time?
xe *06.0000,5000,10 xe 06.02
x06.2ln
yearsx 55.1106.0
2ln
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Ex.10 I have Ex.10 I have $2,500$2,500 to invest and need to invest and need $4,000$4,000 in in 6 years6 years. I found an . I found an account that pays 8% interest (compounded daily)account that pays 8% interest (compounded daily)
B) What is the minimum rate I need to guarantee reaching this value?B) What is the minimum rate I need to guarantee reaching this value?
6*365
3651500,24000
x2190
36516.1
x
36516.16.1 2190
12190 x
3651000214637.1
x
%83.707834.0 x
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Example 11Example 11I want to retire with $1,000,000 in thirty I want to retire with $1,000,000 in thirty
years. I can get a rate of 7%. How much years. I can get a rate of 7%. How much will I need to invest now if it is will I need to invest now if it is compounded monthly? compounded monthly?
30*12
12
07.011000000
x
360005833.11000000 x
86.205,123$x
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Example 11 (contExample 11 (cont’’d)d)
You Try…What about if “Continuously”?You Try…What about if “Continuously”?
30*07.1000000 xe
1.21000000 xe
43.456,122$x