Question 1

A debt of $2000 due four years from now is to be repaid by a payment of $1000 now and a second payment at the end of two years.How much should the second payment be if the interest rate is 5% compounded annually?

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Question 2

A debt of $2000 due in one year is to be repaid by a payment due two years from now and a final payment of $1000 three years from now.If the interest is at the rate of 4% compounded annually,then the payment due in two years is
A) $1000.00.
B) $1118.46.
C) $1155.43.
D) $1191.00.
E) $1203.14.

Accepted Answer

We can use the time value of money formulas to solve the problem. Let X be the payment due in two years. Then we have:

X/(1+0.04) + 1000/(1+0.04)^2 = 2000/(1+0.04)^3

Solving for X, we get:

X = 2000/(1+0.04)^3 - 1000/(1+0.04)^2 = $1118.46 (rounded to the nearest cent)

Question 3

If $4,200 is invested at an annual rate of 5.4% compounded monthly for 10 years,find the compound amount.

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Question 4

If $5,600 is invested at an effective rate of 2.1% for 17 years,what is the compound amount?

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Question 5

If $2,575 is invested at an A.P.R.of 7% compounded semiannually for 15 years,find the accumulated amount.

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Question 6

If $10,000 is invested at an effective rate of 4.25% for 8 years,what is the accumulated amount?

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Question 7

Find the present value of $300 due after six years if the interest rate is 5.4% compounded monthly.

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Question 8

A bank pays 4% annual interest compounded quarterly.How large a deposit must be made now in order that the account contains $1500 at the end of 3 years?

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Question 9

To purchase land for an industrial site,a company agrees to pay $20,000 down and $10,000 at the end of every six-month period for 10 years.If the interest rate is 10% compounded semiannually,what is the corresponding cash value of the land?

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Question 10

For an initial investment of $10,000,suppose a company guarantees the following cash flows at the end of the indicated years:
Year Cash Flow
1 $4000
3 $8000
Assume an interest rate of 5% compounded annually.(a)Determine the net present value of the cash flows.(b)Is the investment profitable?

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Question 11

If $14,300 is invested at an A.P.R.of 8.25% compounded semiannually for 3 years,find a)the compound amount,and b)the compound interest.

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Question 12

Find the present value of $5000 due in 3 years if the interest rate is  
% compounded monthly.

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Question 13

Find the present value of $3000 due after five years if the interest rate is 9.6% compounded semiannually.

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Question 14

A bank charges 0.5 % service fee on checking accounts.If $ 1,000 was deposited in such account,use the concept of negative interest rate to find an approximate value of the amount in this account after 10 years.

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Question 15

A person has the option of satisfying a debt by either paying $5000 now and $5000 in two years,or by paying $3000 now,$3000 a year from now,and a final payment of x dollars two years from now.Determine an equation of value that corresponds to the value of all payments at the end of two years.It is not necessary to solve the equation.Assume that interest is at the rate of 10% compounded semiannually.

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Question 16

You have a choice of two banks.One bank pays interest at 5.54% compounded monthly and the other bank pays interest at 5.53% compounded daily (365 times a year).Which is the better choice? How much more would you make in one year if you deposited $1000?

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Question 17

If $3,100 is invested at a nominal rate of 6% compounded quarterly for 7 years,find a)the compound amount,and b)the compound interest.

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Question 18

You have two investment opportunities.You can invest $6000 at 12% compounded monthly or you can invest $6100 at 12.1% compounded quarterly.Which has the better effective rate of interest? Use a graphing calculator to graph both amounts as a function of time in years.Which is the better investment over twenty years?

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Question 19

Determine the present value of $4000 due in 5 years if the interest rate is 10% compounded semiannually.

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Question 20

If $1,000 is invested at a nominal rate of 4% compounded quarterly for 5 years,find the compound amount.

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Quiz 6: Mathematics of Finance