Question 1

How much must be invested now at 6.5% per year compounded quarterly, to fund an annuity of 15 quarterly payments of $500 each, the first payment being three months after the initial investment?

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Question 2

A farmer wants to borrow $50,000 in order to buy a tractor. She wants to repay the loan by semi-annual installments for six years. If the interest rate is 10% per year compounded semi-annually, what is the amount of each payment?

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Question 3

How much money must be invested now at 16% per year compounded quarterly, to fund an annuity of $20$ quarterly payments of $\$ 1000$ each, the first payment being three months after the initial investment?

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Question 4

What is the monthly payment on a 20 year mortgage of $85,000 at 9% interest per year, compounded monthly? What is the total amount paid on this loan over the 20 year period?

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Question 5

A couple can afford to pay $825 per month toward buying a house. If the mortgage rate is 6.25% and they intend to secure a 15year mortgage, how much can they borrow? How much can they borrow if they intend on securing a 30 year mortgage?

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Question 6

Find the amount of an annuity that consists of 8 monthly payments of $1200 each into an account that pays $24 \%$ interest per year.

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Question 7

Kristi decides to buy a new car for $25,000 and make payments of $525 per month for 6 years. What interest rate is she paying on the loan?

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Question 8

Use mathematical induction to prove that the formula $1 \cdot 3 + 2 \cdot 4 + 3 \cdot 5 + \cdots + n ( n + 2 ) = \frac { n ( n + 1 ) ( 2 n + 7 ) } { 6 }$ is true for all natural numbers $n$ .

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Question 9

Find the amount of an annuity that consists of 15 annual payments of $200 each into an account that pays $12 \%$ interest per year.

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Question 10

Find the amount of an annuity that consists of 52 weekly payments of $10 each into an account that pays 3% interest per year.

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Question 11

Dr. Stevens is considering a 30-year mortgage at 4% interest. She can make payments of $3500 a month. What size loan can she afford?

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Question 12

How much money should be invested monthly at 6% per year, compounded monthly, in order to have $\$ 10,000$ in two years?

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Question 13

What is the monthly payment on a 50 year mortgage of $500,000 at 12% interest per year, compounded monthly? What is the total amount paid on this loan over the 50 year period?

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Question 14

Mike buys a stereo by paying $50 a month for two years. If the interest rate is 12% per year, compounded monthly, what is the price of the stereo?

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Question 15

Find the amount of an annuity that consists of 30 annual payments of $500 each into an account that pays $7 \%$ interest per year.

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Question 16

Use mathematical induction to prove that the sum of a partial geometric sequence is $\frac { a \left( 1 - r ^ { n } \right) } { 1 - r }$ .

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Question 17

How much money should be invested monthly at 18% per year, compounded monthly, in order to have $\$ 2000$ in ten months?

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Question 18

How much money must be invested now at 5% per year compounded semi-annually, to fund an annuity of $14$ semi-annual payments of $\$ 100$ each, the first payment being six months after the initial investment?

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Question 19

Alyson buys a computer by paying $15 a week for three years. If the interest rate is 10.4% per year, compounded weekly, what is the price of the computer?

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Question 20

Dr. Stevens is considering a 30-year mortgage at 6% interest. She can make payments of $2500 a month. What size loan can she afford?

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Quiz 12: Sequences and Series

How much must be invested now at 6.5% per year compounded quarterly, to fund an annuity of 15 quarterly payments of $500 each, the first payment being three months after the initial investment?

A farmer wants to borrow $50,000 in order to buy a tractor. She wants to repay the loan by semi-annual installments for six years. If the interest rate is 10% per year compounded semi-annually, what is the amount of each payment?

How much money must be invested now at 16% per year compounded quarterly, to fund an annuity of 202020 quarterly payments of $1000\$ 1000$1000 each, the first payment being three months after the initial investment?

What is the monthly payment on a 20 year mortgage of $85,000 at 9% interest per year, compounded monthly? What is the total amount paid on this loan over the 20 year period?

A couple can afford to pay $825 per month toward buying a house. If the mortgage rate is 6.25% and they intend to secure a 15year mortgage, how much can they borrow? How much can they borrow if they intend on securing a 30 year mortgage?

Find the amount of an annuity that consists of 8 monthly payments of $1200 each into an account that pays 24%24 \%24% interest per year.

Kristi decides to buy a new car for $25,000 and make payments of $525 per month for 6 years. What interest rate is she paying on the loan?

Use mathematical induction to prove that the formula 1⋅3+2⋅4+3⋅5+⋯+n(n+2)=n(n+1)(2n+7)61 \cdot 3 + 2 \cdot 4 + 3 \cdot 5 + \cdots + n ( n + 2 ) = \frac { n ( n + 1 ) ( 2 n + 7 ) } { 6 }1⋅3+2⋅4+3⋅5+⋯+n(n+2)=6n(n+1)(2n+7)​ is true for all natural numbers nnn .

Find the amount of an annuity that consists of 15 annual payments of $200 each into an account that pays 12%12 \%12% interest per year.

Find the amount of an annuity that consists of 52 weekly payments of $10 each into an account that pays 3% interest per year.

Dr. Stevens is considering a 30-year mortgage at 4% interest. She can make payments of $3500 a month. What size loan can she afford?

How much money should be invested monthly at 6% per year, compounded monthly, in order to have $10,000\$ 10,000$10,000 in two years?

What is the monthly payment on a 50 year mortgage of $500,000 at 12% interest per year, compounded monthly? What is the total amount paid on this loan over the 50 year period?

Mike buys a stereo by paying $50 a month for two years. If the interest rate is 12% per year, compounded monthly, what is the price of the stereo?

Find the amount of an annuity that consists of 30 annual payments of $500 each into an account that pays 7%7 \%7% interest per year.

Use mathematical induction to prove that the sum of a partial geometric sequence is a(1−rn)1−r\frac { a \left( 1 - r ^ { n } \right) } { 1 - r }1−ra(1−rn)​ .

How much money should be invested monthly at 18% per year, compounded monthly, in order to have $2000\$ 2000$2000 in ten months?

How much money must be invested now at 5% per year compounded semi-annually, to fund an annuity of 141414 semi-annual payments of $100\$ 100$100 each, the first payment being six months after the initial investment?

Alyson buys a computer by paying $15 a week for three years. If the interest rate is 10.4% per year, compounded weekly, what is the price of the computer?

Dr. Stevens is considering a 30-year mortgage at 6% interest. She can make payments of $2500 a month. What size loan can she afford?

How much money must be invested now at 16% per year compounded quarterly, to fund an annuity of $20$ quarterly payments of $\$ 1000$ each, the first payment being three months after the initial investment?

Find the amount of an annuity that consists of 8 monthly payments of $1200 each into an account that pays $24 \%$ interest per year.

Use mathematical induction to prove that the formula $1 \cdot 3 + 2 \cdot 4 + 3 \cdot 5 + \cdots + n ( n + 2 ) = \frac { n ( n + 1 ) ( 2 n + 7 ) } { 6 }$ is true for all natural numbers $n$ .

Find the amount of an annuity that consists of 15 annual payments of $200 each into an account that pays $12 \%$ interest per year.

How much money should be invested monthly at 6% per year, compounded monthly, in order to have $\$ 10,000$ in two years?

Find the amount of an annuity that consists of 30 annual payments of $500 each into an account that pays $7 \%$ interest per year.

Use mathematical induction to prove that the sum of a partial geometric sequence is $\frac { a \left( 1 - r ^ { n } \right) } { 1 - r }$ .

How much money should be invested monthly at 18% per year, compounded monthly, in order to have $\$ 2000$ in ten months?

How much money must be invested now at 5% per year compounded semi-annually, to fund an annuity of $14$ semi-annual payments of $\$ 100$ each, the first payment being six months after the initial investment?