1.5 - investments involving regular...
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1.5 Investments involving regular payments.notebook
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Applied Math 40S1.5 – Investments Involving Regular Payments
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Investments Involving Regular Payments
• The future value of an investment with regular deposits or payments is the sum of all the payments or deposits plus the accumulated interest.• You can solve problems about the future value of an investment with regular payments using spreadsheet software or the financial application on a graphing calculator or spreadsheet.
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Investments Involving Regular Payments
• To determine the future value of an investment with n equal regular payments of R dollars, add the future values of all the regular payments.• A= (1+ ) 0 + (1+ ) 1 + (1+ ) 2 +• (1+ ) 3 +…+ (1+ ) −1 • WHERE• A is the future value or the amount of the investment• R is the regular payment• i is the interest rate per compounding period (as a decimal)• n is the number of compounding periods
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Investments Involving Regular Payments
• The future value of a single deposit is greater than the future value for a series of regular payments of the same total amount.• A small deposit invested at a compound interest can earn more money over a long term than a large deposit over a short term.
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Example #1Sophia deposits $750 into her savings account at the
end of each 3month period. The account earns 2.8% interest, compounded quarterly.
How much money will be in the account at the end of 3 years? How much of this money will be earned
interest?Sophia needs at least $6500 for a trip to China. Will
she have enough after 2 years?
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Example #2Michael is saving up to buy a combination washer
and dryer in 2 years. He plans to deposit the same amount at the end of each month into an account
that pays 1.9%, compounded annually.What regular payments must Michael make at the
end of each month to meet his goal of $1300?What interest will he earn?
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Investments Involving Regular Payments
• To simplify this process …• A= [ 1+ −1] • WHERE• A is the future value or the amount of the investment• R is the regular payment• i is the interest rate per compounding period (as a decimal)• n is the number of compounding periods
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Practice #1Determine the future value of weekly payments of
$40 deposited into an account that pays 1.6% interest, compounded weekly, for 2 years.
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Practice #2Determine the future value of monthly payments
of $300 into an account that pays 5.6% interest, compounded monthly, for 20 years.
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Practice #3Determine the future value of quarterly payments of $1000 into an account that pays 4.9% interest,
compounded quarterly, for 18 years.
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Practice #4Determine the future value of annual payments of
$6000 into an account that pays 4.9% interest, compounded annually, for 30 years.
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Practice #5Determine the regular monthly payment required
to have $5000 at the end of 3 years if the investment earns 4.15% interest, compounded
monthly.
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Practice #6Maria wants to buy a moped in 3 years, when she
turns 21. She deposits $120 every month into a savings account that earns 2.25% interest,
compounded monthly. How much money will she have to buy her moped when she is 21? How much
interest will she have earned?
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Practice #7What interest rate, compounded daily, is required to
make daily payments of $1 grow to $1200 in 3 years? Round your answer to two decimal places.
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Practice #8Benjamin is saving for a new oboe costing $2500. He
deposits $50 every month in a savings account that earns 4.6% interest, compounded monthly. How
much money will he have after 4 years? How much interest will he have earned? Will he have saved up
enough money to buy the oboe in 3.5 years?
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Practice #9Determine the regular semiannual payment
required to have $20,000 at the end of 5 years if the investment earns 5.25% interest, compounded semi
annually.$3795.44$1774.96$1953.20$1960.94
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Practice #10Regular semiannual payments of $600 were
deposited into an account paying 6.25% interest, compounded semiannually. If the final value of the account is $23,000, how long was the money
invested?12.8 years25.6 years
10 yearsNone is correct
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Practice #11Regular quarterly payments of $8000 are
deposited into an account paying 3.29% interest, compounded quarterly. If the final value of the
account is $60,000, for how long was the money invested.7.3 years14 years1.8 years3.7 years