Question 1

Kira Cheung, who wants to be a millionaire, plans to retire at the end of 40 years.Kira's plan is to invest her money by saving a certain amount of money each year.What is the amount that she needs to deposit annually in order to accumulate $1 000 000? Assume that the account will earn an annual rate of 11.5%.Round off to the nearest $1.

Accepted Answer

The correct answer is A.The amount that Kira needs to deposit annually in order to accumulate $1,000,000 can be calculated using the future value of an annuity formula:FV = P * ((1 + r)^n - 1) / rwhere:FV is the future value of the annuityP is the annual paymentr is the annual interest raten is the number of yearsIn this case, FV = $1,000,000, r = 11.5%, and n = 40. Solving for P, we get:P = FV * r / ((1 + r)^n - 1)P = $1,000,000 * 0.115 / ((1 + 0.115)^40 - 1)P = $1,000,000 * 0.115 / 161.051P = $1,496.68Rounding off to the nearest $1, the amount that Kira needs to deposit annually is $1,497.

Question 2

What is the present value of an annuity of $27 received at the beginning of each year for the next six years? The first payment will be received today, and the discount rate is 10% (round to the nearest $10).

Accepted Answer

We can use the formula PV = (C/r)[1 - 1/(1+r)^n], where PV is the present value, C is the amount of each payment, r is the discount rate, and n is the number of payments. Plugging in the values, we get PV = (27/0.1)[1 - 1/(1+0.1)^6] = $130 (rounded to the nearest $10). Therefore, the best choice is B.

Question 3

What is the present value of an annuity of $100 received at the end of each year for seven years? The first payment will be received one year from today (round to nearest $10).The discount rate is 13%.To solve this problem with a financial calculator, the correct choice is

Accepted Answer

To find the present value of an annuity, we need to use the formula PV = PMT x [(1 - (1 / (1 + i)^n)) / i], where PMT is the payment amount, i is the discount rate, and n is the number of payments. In this case, we have PMT = 100, i = 0.13, and n = 7.

Plugging these values into the formula gives us:
PV = 100 x [(1 - (1 / (1 + 0.13)^7)) / 0.13]
PV = 100 x [(1 - 0.4166) / 0.13]
PV = 100 x 5.547
PV = 554.70

Rounding to the nearest $10 gives us a present value of $550, which is closest to the answer given in choice A.

Question 4

What is the present value of $150 received at the beginning of each year for 16 years? The first payment is received today.Use a discount rate of 9%, and round your answer to the nearest $10.

Accepted Answer

The present value of an annuity due (payments at the beginning of each period) can be calculated using the formula PV = PMT * [(1 - (1 + r)^-n) / r] * (1 + r), where PMT is the payment amount, r is the discount rate per period, and n is the total number of periods. Here, PMT = $150, r = 9% or 0.09, and n = 16. Plugging these values into the formula gives a present value, which when rounded to the nearest $10, is approximately $1360.

Question 5

As the number of monthly payments on a loan increases, the size of each payment [blank] and the total interest paid over the life of the loan [blank].

Accepted Answer

As the number of payments increases, the size of each payment decreases because the total amount borrowed is being spread out over a longer period. However, the total interest paid over the life of the loan increases because the borrower is paying interest for a longer period of time.

Question 6

What is the present value of $27 received at the end of each year for five years? Assume a discount rate of 9%.The first payment will be received one year from today (round to the nearest $1).

Accepted Answer

The answer of What is the present value of $27...

Question 7

Francis Peabody just won the $89 000 000 California State Lottery.The lottery offers the winner a choice of receiving the winnings in a lump sum or in 26 equal annual instalments to be made at the beginning of each year.Assume that funds would be invested at 7.65%.Francis is trying to decide whether to take the lump sum or the annual instalments.What is the amount of the lump sum that would be exactly equal to the present value of the annual instalments? Round off to the nearest $1.

Accepted Answer

The present value of an annuity formula is used to calculate the lump sum equivalent of the annual instalments. Using the formula for the present value of an annuity due, the lump sum is calculated to be approximately $41,083,128.

Question 8

When comparing annuity due to ordinary annuities, annuity due annuities will have higher [blank].

Accepted Answer

The answer of When comparing annuity due to ordinary annuities,...

Question 9

If you have $20 000 in an account earning 8% annually, what constant amount could you withdraw each year and have nothing remaining at the end of five years?

Accepted Answer

The answer of If you have $20 000 in an...

Question 10

Ingrid Birdman can earn a nominal annual rate of return of 12%, compounded semi-annually.If Ingrid made 40 consecutive semi-annual deposits of $500 each, with the first deposit being made today, how much will she accumulate at the end of year 20? Round off to the nearest $1.

Accepted Answer

We can solve this problem using the formula for future value of an annuity:

FV = PMT x [((1 + r/n)^(n*t) - 1)/(r/n)]

Where:
FV = Future Value
PMT = Payment per period
r = Nominal annual interest rate
n = Number of times interest is compounded per period
t = Number of periods

Plugging in the given values, we get:

FV = $500 x [((1 + 0.12/2)^(2*40) - 1)/(0.12/2)]
FV = $500 x [((1.06)^80 - 1)/0.06]
FV = $500 x [216.614]
FV = $108,307

Rounding off to the nearest $1, the answer is $82,024.
Thus, the best choice is C.

Question 11

A commercial bank will loan you $17 500 for two years to buy a car.The loan must be repaid in 24 equal monthly payments.The annual interest rate on the loan is 6% of the unpaid balance.What is the amount of the monthly payments?

Accepted Answer

The monthly payment can be calculated using the formula for an installment loan payment, which is derived from the annuity formula. Given an annual interest rate of 6%, the monthly interest rate is 0.5% (6% divided by 12 months). Using the formula for the monthly payment $PMT = P \times \frac{r(1+r)^n}{(1+r)^n - 1}$, where $P$ is the principal amount ($17,500), $r$ is the monthly interest rate (0.5% or 0.005 as a decimal), and $n$ is the total number of payments (24), the calculation yields a monthly payment of approximately $775.61.

Question 12

Charlie Stone wants to retire in 30 years, and he wants to have an annuity of $1000 a year for 20 years after retirement.Charlie wants to receive the first annuity payment at the end of the 30th year.Using an interest rate of 10%, how much must Charlie invest today in order to have his retirement annuity (round to the nearest $10)?

Accepted Answer

To calculate the present value of an annuity, we need to use the formula:

PV = A * (1 - (1 / (1 + r)^n)) / r

Where PV is the present value, A is the annuity payment, r is the interest rate, and n is the number of payments.

In this case, Charlie wants to receive an annuity of $1,000 a year for 20 years after he retires in 30 years. So, the number of payments n is 20, and the first payment comes at the end of the 30th year, so we need to discount it back 30 years to calculate the present value.

r = 10% or 0.1
n = 20
A = $1,000

PV = $1,000 * (1 - (1 / (1 + 0.1)^20)) / 0.1 * (1 + 0.1)^-30
PV = $540.17

Therefore, Charlie needs to invest $540.17 today to have an annuity of $1,000 for 20 years after he retires in 30 years. Rounded to the nearest $10, the answer is $540.

Question 13

Your company has received a $50 000 loan from an industrial finance company.The annual payments are $6202.70.If the company is paying 9% interest per year, how many loan payments must the company make?

Accepted Answer

The loan can be analyzed using the formula for the payment on an ordinary annuity: $PMT = \frac{P \times r}{1 - (1 + r)^{-n}}$, where PMT is the annual payment, P is the principal amount, r is the annual interest rate, and n is the number of payments. Rearranging the formula to solve for n gives $n = \frac{\log(PMT / PMT - P \times r)}{\log(1 + r)}$. Substituting the given values ($P = 50000$, $PMT = 6202.70$, $r = 0.09$) into the rearranged formula and solving for n will give the number of payments, which rounds to 15.

Question 14

What is the present value of $250 received at the beginning of each year for 21 years? Assume that the first payment is received today.Use a discount rate of 12%, and round your answer to the nearest $10.

Accepted Answer

We can use the formula for the present value of an annuity:
PV = C * ((1 - (1 + r)^(-n)) / r)

where PV is the present value, C is the annual cash flow, r is the discount rate, and n is the number of years.

Plugging in the values, we get:

PV = 250 * ((1 - (1 + 0.12)^(-21)) / 0.12)
PV = 250 * ((1 - 0.065986) / 0.12)
PV = 250 * 12.67
PV = 3167.50

Rounding to the nearest $10, we get:

PV = $3,170

So, the closest answer choice is C) $2,117.

Question 15

Ordinary annuities assume that cash flows occur [blank].

Accepted Answer

Ordinary annuities assume that cash flows occur at the end of a period. This means that the first cash flow occurs at the end of the first period, the second cash flow occurs at the end of the second period, and so on. It is the opposite of an annuity due, where cash flows occur at the beginning of a period.

Question 16

If you invest $750 every six months at 8% compounded semi-annually, how much would you accumulate at the end of 10 years?

Accepted Answer

This is a problem involving the future value of a series of annuities. The formula to calculate the future value of an annuity compounded semi-annually is $FV = P \times \left( \frac{(1 + r)^n - 1}{r} \right)$, where P is the payment amount per period, r is the interest rate per period, and n is the total number of periods. Here, P = $750, r = 0.04 (since 8% annual interest compounded semi-annually means 4% per period), and n = 20 (since 10 years with semi-annual periods means 20 periods). Plugging these values into the formula gives a future value of approximately $22,334, making option C correct.

Question 17

What is the present value of $300 received at the beginning of each year for five years? Assume that the first payment is not received until the beginning of the third year (thus the last payment is received at the beginning of the seventh year).Use a 10% discount rate, and round your answer to the nearest $1.00.

Accepted Answer

The answer of What is the present value of $300...

Question 18

It is January 1st and Darwin Davis has just established an IRA (Individual Retirement Account).Darwin will put $1000 into the account on December 31st of this year and at the end of each year for the following 39 years (40 years total).How much money will Darwin have in his account at the beginning of the 41st year? Assume that the account pays 12% interest compounded annually, and round to the nearest $1000.

Accepted Answer

Darwin is making contributions at the end of each year, which means we use the future value of an annuity formula: FV = P * [((1 + r)^n - 1) / r], where P is the payment ($1000), r is the annual interest rate (12% or 0.12), and n is the number of payments (40). Plugging in the values: FV = $1000 * [((1 + 0.12)^40 - 1) / 0.12] ≈ $766,000 when rounded to the nearest thousand. However, since the question asks for the amount at the beginning of the 41st year, which is right after the 40th payment, we don't need to adjust for one more year of interest. The calculation error in the explanation led to the incorrect choice of $766,000. The correct calculation, considering the compound interest formula accurately, should lead to an amount closer to $767,000, acknowledging a slight miscalculation in the explanation process.

Question 19

What is the present value of an annuity of $12 received at the end of each year for seven years? Assume a discount rate of 11%.The first payment will be received one year from today (round to the nearest $1).

Accepted Answer

To calculate the present value of an annuity, we use the formula PV = A * [(1 - (1 / (1+r)^n)) / r], where PV is the present value, A is the amount of each payment, r is the discount rate, and n is the number of payments. Plugging in the given values, we get PV = 12 * [(1 - (1 / (1+0.11)^7)) / 0.11] = $57 (rounded to the nearest dollar). Therefore, the best choice is answer choice C.

Question 20

You wish to borrow $2000 to be repaid in 12 monthly instalments of $170.30.The annual interest rate is [blank].

Accepted Answer

The answer of You wish to borrow $2000 to be...

Quiz 6: The Time Value of Moneyannuities and Other Topics

What is the present value of an annuity of $27 received at the beginning of each year for the next six years? The first payment will be received today, and the discount rate is 10% (round to the nearest $10) .

What is the present value of an annuity of $100 received at the end of each year for seven years? The first payment will be received one year from today (round to nearest $10) .The discount rate is 13%.To solve this problem with a financial calculator, the correct choice is