Question 1

Heather is planning to invest a constant amount of money at the end of every year for 15 years and then allow her money to accumulate interest for 15 more years without any additional deposits. If her investments earn 11% compounded annually and she must have $650,000 in 30 years, how much will she invest at the end of each of the next 15 years?

Accepted Answer

E

Question 2

Fred must pay a $25,000 obligation one year from now. What end-of-month payments for twelve months would put the creditor in an equivalent financial position if the creditor can earn 9% compounded monthly?

Accepted Answer

The monthly payment can be calculated using the formula for the present value of an annuity. The present value of the annuity should equal the $25,000 obligation. Using the formula: PV = PMT * [(1 - (1 + r)^-n) / r], where PV = $25,000, r = 0.09/12, and n = 12, the correct monthly payment is approximately $1,998.79.

Question 3

If you have $45,000 earning 9.6% compounded monthly, how much money could you take out of the investment at the end of every year for 10 years?

Accepted Answer

To solve this, we use the formula for the annuity payment from a present value, which is P = [rPV] / [1 - (1 + r)^-n], where P is the payment, PV is the present value, r is the monthly interest rate, and n is the total number of payments. Here, PV = $45,000, r = 9.6% annual interest rate compounded monthly (which is 0.096/12 per month), and n = 10 years * 12 months/year = 120 months. Plugging these values into the formula gives us the annual withdrawal amount, which is approximately $7,334.

Question 4

What annual deposit should Martina make to her RRSP at the end of every year if the funds earn 12% compounded monthly and her goal is to accumulate $1,000,000 at the end of 25 years?

Accepted Answer

The answer of What annual deposit should Martina make to...

Question 5

Vince has $35,000 to purchase an annuity that will provide him with equal payments at the end of every three months for the next six years. If the funds earn 8% compounded quarterly, what is the size of the quarterly payments he will receive?

Accepted Answer

The size of the quarterly payments can be calculated using the formula for the present value of an annuity: $PV = PMT \times \left[\frac{1 - (1 + r)^{-n}}{r}\right]$, where $PV$ is the present value of the annuity (initial investment), $PMT$ is the payment per period, $r$ is the interest rate per period, and $n$ is the total number of payments. Given that Vince has $35,000 to invest at an 8% annual interest rate compounded quarterly, the quarterly interest rate is $8\% / 4 = 2\%$, or $0.02$ as a decimal. The total number of quarterly payments over six years is $6 \times 4 = 24$. Rearranging the formula to solve for $PMT$ gives us $PMT = PV \times \frac{r}{1 - (1 + r)^{-n}}$. Substituting the given values, we get $PMT = 35000 \times \frac{0.02}{1 - (1 + 0.02)^{-24}}$, which calculates to approximately $1,850. Thus, the size of the quarterly payments Vince will receive is about $1,850.

Question 6

How much will Clarence have to invest at the end of every year at 11% compounded annually if he is going to accumulate $25,000 in five years?

Accepted Answer

To find the annual investment needed, we use the future value of an annuity formula: FV = Pmt * [(1 + r)^n - 1] / r. Solving for Pmt, we get Pmt = FV / [(1 + r)^n - 1] / r. Plugging in FV = $25,000, r = 0.11, and n = 5, we find Pmt ≈ $4,014.25.

Question 7

The interest rate charged on a loan of $85,000 is 7.75% compounded annually. If the loan is to be paid off over seven years, calculate the size of the annual payments.

Accepted Answer

The answer of The interest rate charged on a loan...

Question 8

An investment of $25,000 is made for a 10-year term. After the term expires, equal withdrawals will be made at the end of every month for 15 years. What will the size of the monthly withdrawal be if the investment earns 9% compounded monthly for both the deposit and withdrawal periods.

Accepted Answer

The answer of An investment of $25,000 is made for...

Question 9

What regular investment, made at the end of every three months and earning 10% compounded quarterly, would accumulate to $475,000 in 20 years?

Accepted Answer

The answer of What regular investment, made at the end...

Question 10

A 25-year annuity is purchased for $650,000. Determine the payments it will deliver on a quarterly basis if the rate of interest is 5.05% compounded monthly.

Accepted Answer

To find the quarterly payment, first convert the annual interest rate to a quarterly rate. The monthly rate is 5.05%/12 = 0.4208333%. Convert this to a quarterly rate: (1 + 0.004208333)^3 - 1 = 0.012662. Use the annuity formula: P = A * [(1 - (1 + r)^-n) / r], where P is the present value ($650,000), r is the quarterly rate (0.012662), and n is the total number of payments (25*4 = 100). Solving for A gives approximately $11,504.66.

Question 11

Marvin hopes to accumulate $1,000,000 in his retirement plan by making equal contributions at the end of each month for 35 years. He is planning to earn 10.8% compounded monthly. What amount should he deposit every month?

Accepted Answer

To find the monthly deposit amount for Marvin's retirement plan, we use the formula for the future value of an annuity, which is $FV = P \times \frac{(1 + r)^n - 1}{r}$, where $FV$ is the future value, $P$ is the monthly payment, $r$ is the monthly interest rate, and $n$ is the total number of payments. Here, $FV = \$1,000,000$, annual interest rate $= 10.8\%$, so the monthly interest rate $r = \frac{10.8\%}{12} = 0.9\%$, and $n = 35 \times 12$ months. Rearranging the formula to solve for $P$, and substituting the given values, we find that the correct monthly deposit amount is closest to option B, $213.87.

Question 12

Calculate the size of the monthly mortgage loan payment if a $121,500 loan at 7% compounded semi-annually is to be paid off over 18 years.

Accepted Answer

The correct calculation involves using the formula for a fixed-rate mortgage, which is often represented as $M = P\frac{r(1+r)^n}{(1+r)^n-1}$, where $M$ is the monthly payment, $P$ is the principal loan amount, $r$ is the monthly interest rate (annual rate divided by 12), and $n$ is the total number of payments (years times 12). Given a 7% annual interest rate compounded semi-annually, we first adjust this to a monthly rate by dividing by 12, but since it's compounded semi-annually, we use the effective annual rate formula to adjust the interest rate. However, for simplicity in common mortgage calculations, we directly use the nominal rate divided by 12 for monthly calculations. For an 18-year term, or 216 months, the calculation is plugged into the formula. The closest match to the correct calculation based on the options provided is $983.75.

Question 13

A loan of $17,200 at 9% compounded monthly is to be paid off by equal payments to be made at the end of every month for three years. What is the size of the monthly payment?

Accepted Answer

The answer of A loan of $17,200 at 9% compounded...

Question 14

If a single sum of $25,000 is invested at age 25 at 13% compounded annually, what amount will the investor be able to withdraw from the savings, at the end of every month for 20 years, beginning at age 65? At age 65 the investor will put his money into a safer investment that earns only 6% compounded monthly.

Accepted Answer

The answer of If a single sum of $25,000 is...

Question 15

Vanessa wants to retire in 25 years with enough saved to be able to withdraw $5,000 monthly for 20 years. She has already accumulated $48,000 in her investment account. Assume that the rate of interest is 4.8% compounded annually for the 25 years of her contributions, and changes to 3.6% compounded monthly for the next 20 years. Determine what annual contributions she has to make for the next 25 years in order to meet her objective.

Accepted Answer

The answer of Vanessa wants to retire in 25 years...

Question 16

Today, Barry reached his 50^th birthday and he has $70,000 in his retirement fund. His goal is to have $500,000 on his 65^th birthday. He can expect his investments to earn 13% compounded semi-annually. How much will he have to invest at the end of every six months for the next 15 years in order to reach his goal?

Accepted Answer

The answer of Today, Barry reached his 50^th birthday and...

Question 17

A loan of $45,000 calls for equal payments at the end of every three months for the next six years. What is the size of the payments if the interest rate is 14% compounded semi-annually?

Accepted Answer

The answer of A loan of $45,000 calls for equal...

Question 18

If the invested funds earn 13% compounded quarterly what amount invested at the end of every six months for 15 years will accumulate to $295,000?

Accepted Answer

The future value of an annuity formula is used here, considering the interest is compounded quarterly. The effective semi-annual interest rate is calculated, and the future value of the annuity is set to $295,000. Solving for the periodic payment gives approximately $3,352.

Question 19

Given the time-value of money of 11% compounded annually, calculate the size of the month-end payments for the next five years that would be equivalent to a single payment of $13,285 payable five years from now.

Accepted Answer

To find the monthly payment, we first need to find the present value of the $13,285 due in five years using the formula for present value: PV = FV / (1 + r)^n, where FV is the future value, r is the annual interest rate, and n is the number of years. Then, we use the annuity formula to find the monthly payment: PMT = PV * [r / (1 - (1 + r)^-n)], where r is the monthly interest rate and n is the total number of payments. After calculations, the correct monthly payment is approximately $169.39.

Question 20

Sally has invested a constant amount at the end of every six months for the last 40 years. She has made wise investment decisions and has earned a return of 16.4% compounded semi-annually. Today the value of her savings has reached $2,500,000. What amount has she been investing every half-year?

Accepted Answer

The answer of Sally has invested a constant amount at...

Quiz 11: Annuities: Periodic Payment, Number of Payments, and Interest Rate