Question 1

Find the amount of an ordinary annuity for 8 years of semiannually payments of $1,900 that earn interest at 8%/year compounded semi-annually. Round your answer to the nearest cent.
$__________

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Question 2

Linda has joined a "Christmas Fund Club" at her bank. At the end of every month, December through October inclusive, she will make a deposit of $60 in her fund. If the money earns interest at the rate of 6%/year compounded monthly, how much will she have in her account on December 1 of the following year? Round your answer to the nearest cent.
$ __________

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Question 3

Find the present value of an ordinary annuity of $50 payments each made monthly over 10 years and earning interest at 4% per year compounded monthly. Round your answer to the nearest cent.
$__________

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Question 4

Robin, who is self-employed, contributes $5,500/year into a Keogh account. How much will he have in the account after 15 years if the account earns interest at the rate of 8.5%/year compounded yearly? Please round the answer to the nearest cent.
$ __________

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Question 5

Find the present value of an ordinary annuity of $1,300 payments each made semiannually over 6 years and earning interest at 10% per year compounded semi-annually. Round your answer to the nearest cent.
$ __________

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Question 6

If Jackson deposited $400 at the end of each month in the saving account earing interest at the rate of 6%/year compounded monthly, how much will he have on deposite in his savings account at the end of 6 years, assuming that he makes no withdrawals during that period? Round your answers to two decimal places. ​

Accepted Answer

The correct answer is A because the future value of an annuity is calculated using the formula FV = P * ((1 + r/n)^(n*t) - 1) / (r/n), where P is the periodic payment, r is the annual interest rate, n is the number of compounding periods per year, and t is the number of years. In this case, P = $400, r = 6%, n = 12 (since interest is compounded monthly), and t = 6. Plugging these values into the formula, we get FV = $34,563.54.

Question 7

If a merchant deposits $500 annually at the end of each tax year in an IRA account paying interest at the rate of 8%/year compounded annually, how much will she have in her account at the end of 20 years? Round your answer to the nearest cent.
$ __________

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Question 8

As a fringe benefit for the past 12 years, Colin's employer has contributed $50 at the end of each month into an employee retirement account for Colin that pays interest at the rate of 7%/year compounded monthly. Colin has also contributed $1,500 at the end of each of the last 6 years into an IRA that pays interest at the rate of 8%/year compounded yearly. How much does Colin have in his retirement fund at this time? Please round the answer to the nearest cent.
$ __________

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Question 9

Find the present value of an ordinary annuity of $600 payments each made quarterly over 5 years and earning interest at 12% per year compounded quarterly. Round your answer to the nearest cent.
$ __________

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Question 10

Mike's Sporting Goods sells elliptical trainers under two payment plans: cash and installment. Under the installment plan, the customer pays $90/month over 5 years with interest changed on the balance at a rate of 19%/year compounded monthly. Find the cash price for an elliptical trainer if it is equivalent to the price paid by a customer using the installment plan. Round your answers to two decimal places. ​

Accepted Answer

We can use the present value formula to find the cash price equivalent to the installment plan payments. Let P be the cash price we want to find.

PV = (C/r) * [1 - (1+r)^(-n)],

where C is the monthly payment, r is the monthly interest rate (19%/12 = 1.58%), n is the number of months (5 years * 12 months/year = 60), and PV is the present value.

Substituting the values, we get:

P = PV = (90/1.005^60) * [1 - (1.005)^(-60)]/0.0158
P ≈ $3,469.47

Therefore, the best choice is A.

Question 11

Lupe made a down payment of $1,500 toward the purchase of a new car. To pay the balance of the purchase price, she has secured a loan from her bank at the rate of 12%/year compounded monthly. Under the terms of her finance agreement, she is required to make payments of $240/month for 48 mo. What is the cash price of the car? Round your answer to the nearest cent.
$ __________

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Question 12

Find the present value of an ordinary annuity of $5,000 payments each made annually over 9 years and earning interest at 9% per year compounded annually. Round your answer to the nearest cent.
$ __________

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Question 13

Joe plans to deposite $100 at the end of each month into a bank acount for a period of 2 years, after which he plans to deposite $600 at the end of each month into the same account for another 3 years. If the bank pays interest at the rate of 8%/year compounded monthly, how much will Joe have in his account by the end of 5 years? (Assume no withdrawals are made during the 5-years period.) Round your intermediate calculations to two decimal places. ​

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Question 14

The Betzes have leased an auto for 1 yr at $600/month. If money is worth 8%/year compounded monthly, what is the equivalent cash payment (present value) of this annuity? Please round your answer to the nearest cent.
$ __________

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Question 15

The Jonsons have accumulated the nest egg of $30,000 that they indent to use as a down payment towards the purchase of a new house. Because their present gross income has placed them in a relative high tax bracket, they have decided to invest a minimum of $2,600/month monthly payments ( to take the advantages of the tax deduction) towards the purchase of their house. However, because of other defalt obligation their monthly payment should be exceed $4,000. If local morgage rates are 4% compounded monthly for a conventional 30-years morgage, how would this affect the price range of houses that the Jonsons should be consider? Round your intermediate calculations to two decimal places and the final answer to nearest integer. ​

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Question 16

Find the amount of an ordinary annuity for  years of weekly payments of $  that earn interest at  % per year compounded weekly. Round your answer to the nearest cent.
$__________

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Question 17

Lauren plans to deposit $7,000 into a bank account at the beginning of next month and $400/month into the same account at the end of that month and at the end of each subsequent month for the next 4 yr. If her bank pays interest at the rate of 5%/year compounded monthly, how much will Lauren have in her account at the end of the 4 yr? (Assume she makes no withdrawals during the 4-yr period.) Please round the answer to the nearest cent. ​

Accepted Answer

Lauren's account grows through two methods: an initial lump sum deposit and regular monthly deposits. The future value of her account can be calculated using the future value formula for a lump sum and the future value formula for an annuity.1. **Future Value of the Lump Sum (Initial $7,000 Deposit):**$$FV_{lump} = P(1 + r/n)^{nt}$$Where:- $P = \$7,000$ (initial deposit),- $r = 0.05$ (annual interest rate),- $n = 12$ (compounding periods per year),- $t = 4$ (years).$$FV_{lump} = 7000(1 + 0.05/12)^{12*4}$$$$FV_{lump} = 7000(1.0041667)^{48}$$$$FV_{lump} = 7000(1.2213869)$$$$FV_{lump} ≈ \$8,549.71$$2. **Future Value of Regular Monthly Deposits:**$$FV_{annuity} = PMT \left(\frac{(1 + r/n)^{nt} - 1}{r/n}\right)$$Where:- $PMT = \$400$ (monthly deposit),- $r = 0.05$ (annual interest rate),- $n = 12$ (compounding periods per year),- $t = 4$ (years).$$FV_{annuity} = 400 \left(\frac{(1 + 0.05/12)^{12*4} - 1}{0.05/12}\right)$$$$FV_{annuity} = 400 \left(\frac{(1.0041667)^{48} - 1}{0.0041667}\right)$$$$FV_{annuity} = 400(21.5063)$$$$FV_{annuity} ≈ \$21,202.52$$3. **Total Future Value:**$$FV_{total} = FV_{lump} + FV_{annuity}$$$$FV_{total} ≈ \$8,549.71 + \$21,202.52$$$$FV_{total} ≈ \$29,752.23$$Rounding to the nearest cent, Lauren will have approximately $29,752.22 in her account at the end of the 4 years, which matches choice B.

Question 18

The Jonsons have accumulated the nest egg of $10,000 that they indent to use as a down payment towards the purchase of a new house. Because their present gross income has placed them in a relative heigh tax bracket, they have decided to invest a minimum of $2,800/month monthly payments ( to take the advantages of the tax deduction) towards the purchase of their house. However, because of other defalt obligation their monthly payment should not exceed $4,000. If Jonson decide to secure a 15-years mortgage istead of a 30- years mortgage, what is the price range of houses they should consider when the local morgage rates for this type of loan is 7% ? Round your answers to nearest integer. ​

Accepted Answer

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Question 19

Find the amount of an ordinary annuity of 10 yearly payments of $1,700 that earn interest at 10% per year compounded annually. Round your answer to the nearest cent.
$ __________

Accepted Answer

The answer of Find the amount of an ordinary annuity...

Question 20

Find the amount of an ordinary annuity for 6 years of quarterly payments of $2,200 that earn interest at 8% per year compounded quarterly. Round your answer to the nearest cent.
$__________

Accepted Answer

The answer of Find the amount of an ordinary annuity...

Quiz 5: Mathematics of Finance

Find the amount of an ordinary annuity for 8 years of semiannually payments of $1,900 that earn interest at 8%/year compounded semi-annually. Round your answer to the nearest cent. $__________

Find the present value of an ordinary annuity of $50 payments each made monthly over 10 years and earning interest at 4% per year compounded monthly. Round your answer to the nearest cent. $__________

Robin, who is self-employed, contributes $5,500/year into a Keogh account. How much will he have in the account after 15 years if the account earns interest at the rate of 8.5%/year compounded yearly? Please round the answer to the nearest cent. $ __________

Find the present value of an ordinary annuity of $1,300 payments each made semiannually over 6 years and earning interest at 10% per year compounded semi-annually. Round your answer to the nearest cent. $ __________

If a merchant deposits $500 annually at the end of each tax year in an IRA account paying interest at the rate of 8%/year compounded annually, how much will she have in her account at the end of 20 years? Round your answer to the nearest cent. $ __________

Find the present value of an ordinary annuity of $600 payments each made quarterly over 5 years and earning interest at 12% per year compounded quarterly. Round your answer to the nearest cent. $ __________

Find the present value of an ordinary annuity of $5,000 payments each made annually over 9 years and earning interest at 9% per year compounded annually. Round your answer to the nearest cent. $ __________

The Betzes have leased an auto for 1 yr at $600/month. If money is worth 8%/year compounded monthly, what is the equivalent cash payment (present value) of this annuity? Please round your answer to the nearest cent. $ __________

Find the amount of an ordinary annuity for years of weekly payments of $ that earn interest at % per year compounded weekly. Round your answer to the nearest cent. $__________

Find the amount of an ordinary annuity of 10 yearly payments of $1,700 that earn interest at 10% per year compounded annually. Round your answer to the nearest cent. $ __________

Find the amount of an ordinary annuity for 6 years of quarterly payments of $2,200 that earn interest at 8% per year compounded quarterly. Round your answer to the nearest cent. $__________