Question 1

Using an inheritance he recently received, Sam wants to purchase a deferred annuity that will pay $5000 every three months between age 60 (when he plans to retire) and age 65 (when his permanent pension will begin). The first payment is to be three months after he reaches 60, and the last is to be on his 65^th birthday. If Sam's current age is 50 years and 6 months, and the invested funds will earn 6% compounded quarterly, what amount must he invest in the deferred annuity?

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Question 2

A conditional sale contract requires the debtor to make six quarterly payments of $569, with the first payment due in six months. What amount will a finance company pay to purchase the contract on the date of sale if the finance company requires a rate of return of 16% compounded quarterly?

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Question 3

A $10,000 investment will be allowed to grow at 8.5% compounded semiannually until it can support semiannual withdrawals of $1000 for 20 years. Rounded to the nearest month, how long before the first withdrawal must the investment be allowed to grow?

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Question 4

Mrs. Corriveau has just retired at age 58 with $160,360 in her RRSP. She plans to live off other savings for a few years and allow her RRSP to continue to grow on a tax-deferred basis until there is a sufficient amount to purchase a 25-year annuity paying $2000 at the end of each month. If her RRSP and the annuity each earn 7.5% compounded monthly, how much longer must she let her RRSP grow (before she buys the annuity)?

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Question 5

The nominal interest rate associated with an ordinary general annuity is 7% compounded annually. Rounded to the nearest 0.001%, what is the corresponding periodic rate of interest that matches the payment interval for:
a. Semiannual payments?
b. Quarterly payments?
c. Monthly payments?

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Question 6

The nominal interest rate associated with an ordinary general annuity is 7% compounded semiannually. Rounded to the nearest 0.001%, what is the corresponding periodic rate of interest that matches the
payment interval for:
payment interval for:
a. Annual payments?
b. Quarterly payments?
c. Monthly payments?

Accepted Answer

The answer of The nominal interest rate associated with an...

Question 7

The nominal interest rate associated with an ordinary general annuity is 8% compounded quarterly. Rounded to the nearest 0.001%, what is the corresponding periodic rate of interest that matches the payment interval for:
a. Annual payments?
b. Semiannual payments?
c. Monthly payments?

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The answer of The nominal interest rate associated with an...

Question 8

The nominal interest rate associated with an ordinary general annuity is 8% compounded monthly. Rounded to the nearest 0.001%, what is the corresponding periodic rate of interest that matches the payment interval for:
a. Annual payments?
b. Semiannual payments?
c. Quarterly payments?

Accepted Answer

The answer of The nominal interest rate associated with an...

Question 9

This problem demonstrates the dependence of an annuity's future value on the compounding frequency. Suppose $1000 is invested at the end of each year for 25 years. Calculate the future value if the invested funds earn:
a. 6% compounded annually.
b. 6% compounded semiannually.
c. 6% compounded quarterly.
d. 6% compounded monthly.

Accepted Answer

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Question 10

This problem demonstrates the dependence of an annuity's present value on the compounding frequency. What minimum initial amount will sustain a 25-year annuity paying $1000 at the end of each year if the initial amount can be invested to earn:
a. 6% compounded annually?
b. 6% compounded semiannually?
c. 6% compounded quarterly?
d. 6% compounded monthly?

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Question 11

An ordinary annuity consists of quarterly payments of $400 for 11 years. Based on a nominal rate of 6.5% compounded annually, calculate the annuity's:
a. Present value.
b. Future value.

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Question 12

An annuity consists of end-of-month payments of $150 continuing for 6½ years. Based on a nominal rate of 10% compounded quarterly, calculate the annuity's:
a. Present value.
b. Future value.

Accepted Answer

The answer of An annuity consists of end-of-month payments of...

Question 13

An ordinary annuity consists of semiannual payments of $2750 for a 3½ -year term. Using a nominal rate of 8% compounded monthly, calculate the annuity's:
a. Present value.
b. Future value.

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Question 14

Payments of $1500 will be made at the end of every quarter for 13½ years. Using a nominal rate of 7.5% compounded semiannually, calculate the annuity's:
a. Present value.
b. Future value.

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Question 15

Payments of $3500 will be made at the end of every year for 17 years. Using a nominal rate of 5.25% compounded monthly, calculate the annuity's:
a. Present value.
b. Future value.

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Question 16

An annuity consists of semiannual payments of $950 for a term of 8½ years. Using a nominal rate of 9% compounded quarterly, calculate the ordinary annuity's:
a. Present value.
b. Future value.

Accepted Answer

The answer of An annuity consists of semiannual payments of...

Question 17

A deferred annuity consists of an ordinary annuity paying $2000 semiannually for a 10-year term after a 5-year period of deferral. Calculate the deferred annuity's present value using a discount rate of 7% compounded quarterly.

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Question 18

The first quarterly payment of $750 in a five-year annuity will be paid 3¾ years from now. Based on a discount rate of 8.25% compounded monthly, what is present value of the payments today?

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Question 19

A loan granted today will be repaid by payments of $500 per month running for 3½ years. The first payment is due 2 years and 10 months from today. What amount was borrowed if the interest rate on the loan is 9% compounded quarterly?

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Question 20

What is the future value eight years from now of each of the following cash-flow streams if money can earn 9% compounded semiannually?
a) A single payment of $5000 today.
b) An ordinary annuity starting today with eight annual payments of $900.
c) An ordinary annuity starting in three years with 20 quarterly payments of $400.

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Quiz 10: Ordinary Annuities: Future Value and Present Value

A conditional sale contract requires the debtor to make six quarterly payments of $569, with the first payment due in six months. What amount will a finance company pay to purchase the contract on the date of sale if the finance company requires a rate of return of 16% compounded quarterly?

A $10,000 investment will be allowed to grow at 8.5% compounded semiannually until it can support semiannual withdrawals of $1000 for 20 years. Rounded to the nearest month, how long before the first withdrawal must the investment be allowed to grow?

The nominal interest rate associated with an ordinary general annuity is 7% compounded annually. Rounded to the nearest 0.001%, what is the corresponding periodic rate of interest that matches the payment interval for: a. Semiannual payments? b. Quarterly payments? c. Monthly payments?

The nominal interest rate associated with an ordinary general annuity is 8% compounded quarterly. Rounded to the nearest 0.001%, what is the corresponding periodic rate of interest that matches the payment interval for: a. Annual payments? b. Semiannual payments? c. Monthly payments?

The nominal interest rate associated with an ordinary general annuity is 8% compounded monthly. Rounded to the nearest 0.001%, what is the corresponding periodic rate of interest that matches the payment interval for: a. Annual payments? b. Semiannual payments? c. Quarterly payments?

An ordinary annuity consists of quarterly payments of $400 for 11 years. Based on a nominal rate of 6.5% compounded annually, calculate the annuity's: a. Present value. b. Future value.

An annuity consists of end-of-month payments of $150 continuing for 6½ years. Based on a nominal rate of 10% compounded quarterly, calculate the annuity's: a. Present value. b. Future value.

An ordinary annuity consists of semiannual payments of $2750 for a 3½ -year term. Using a nominal rate of 8% compounded monthly, calculate the annuity's: a. Present value. b. Future value.

Payments of $1500 will be made at the end of every quarter for 13½ years. Using a nominal rate of 7.5% compounded semiannually, calculate the annuity's: a. Present value. b. Future value.

Payments of $3500 will be made at the end of every year for 17 years. Using a nominal rate of 5.25% compounded monthly, calculate the annuity's: a. Present value. b. Future value.

An annuity consists of semiannual payments of $950 for a term of 8½ years. Using a nominal rate of 9% compounded quarterly, calculate the ordinary annuity's: a. Present value. b. Future value.

A deferred annuity consists of an ordinary annuity paying $2000 semiannually for a 10-year term after a 5-year period of deferral. Calculate the deferred annuity's present value using a discount rate of 7% compounded quarterly.

The first quarterly payment of $750 in a five-year annuity will be paid 3¾ years from now. Based on a discount rate of 8.25% compounded monthly, what is present value of the payments today?

A loan granted today will be repaid by payments of $500 per month running for 3½ years. The first payment is due 2 years and 10 months from today. What amount was borrowed if the interest rate on the loan is 9% compounded quarterly?