Question 1

Ten years ago Sandi made a commitment to accumulate $500,000 by investing $350 at the beginning of every month for as long as it takes. For the first 10 years she has been earning 13% compounded semiannually. She is now moving all of her money to a safer investment that will earn 9.6% compounded monthly. She is continuing to invest the $350 per month. How much more time will it take Sandi to reach $500,000?

Accepted Answer

The answer of Ten years ago Sandi made a commitment...

Question 2

A landowner and a developer have agreed on a contract that would give the developer an option to purchase a property at a pre-determined price anytime over the length of the contract. The developer is committed to pay the landowner $25,000 at the beginning of every three months throughout the term of this contract. The present value of the contract, calculated with a rate of 13% compounded semiannually is $319,000. For how many years does the developer have an option to purchase this property?

Accepted Answer

The present value of an annuity formula is used to calculate the number of years. Given the quarterly payment, the interest rate per period is adjusted to reflect quarterly compounding. Solving for the number of periods gives 16 quarters, which corresponds to 4 years.

Question 3

A Term Life Insurance policy requires premium payments of $63 at the beginning of every month. Using a rate of 15% compounded monthly, the present value of the stream of payments is $4,250. What is the term of the policy?

Accepted Answer

The answer of A Term Life Insurance policy requires premium...

Question 4

Marktown Mall has leases with tenants that call for payments of $97,400 at the beginning of every month. The present value of the payments has been calculated at $3,682,300, based on a discount rate of 19.2% compounded monthly. What is the term of the lease contracts?

Accepted Answer

The present value of an annuity formula is used to calculate the term. Given the present value, monthly payment, and monthly discount rate (19.2% annually is 1.6% monthly), solving for the number of periods (n) gives approximately 57 months.

Question 5

For how long will Angela be able to withdraw $5,000 at the beginning of every three months from her retirement fund of $320,000 if she is earning 5.4% compounded monthly?

Accepted Answer

The answer of For how long will Angela be able...

Question 6

Marcellus has been saving $3,600 at the beginning of every year for 27 years. Now, at the end of the 27^th year his investments have reached a value of $606,500. What effective annual rate has he earned on his investments?

Accepted Answer

The answer of Marcellus has been saving $3,600 at the...

Question 7

Investments of $200 at the beginning of every month have accumulated to $405,515 after 30 years. Expressed as a monthly compounded nominal annual rate, what return have these investments provided?

Accepted Answer

The answer of Investments of $200 at the beginning of...

Question 8

Isabel believes that she can accumulate $5,000,000 over 35 years by investing $4,500 at the beginning of every quarter year. What semiannually compounded nominal rate would she need to earn?

Accepted Answer

To find the nominal rate compounded semiannually, we use the future value of an annuity formula. Solving for the rate that makes the future value $5,000,000 with quarterly payments of $4,500 over 35 years, we find that the nominal rate is approximately 9.619%.

Question 9

An insurance company considers the present value of a 10-year term life insurance policy to be $3,738. The premiums that the company collects are $55 at the beginning of every month for the 10 years. What monthly compounded nominal rate is implied in the calculation of the policy's value?

Accepted Answer

The present value of the annuity (premiums) is calculated using the formula for the present value of an annuity. Solving for the interest rate that equates the present value of the annuity to $3,738 gives a monthly compounded nominal rate of 12.900%.

Question 10

The Minnesota Twins Baseball Club has 1.5 years remaining on the lease of a stadium. They are required to pay $950,000 at the beginning of every three months over that time. This is reflected on their balance sheet as a liability of $5,250,000. What is the quarterly compounded nominal rate implied in this calculation?

Accepted Answer

The liability of $5,250,000 reflects the present value of the future lease payments. Given that there are 1.5 years remaining and payments are made quarterly, there are 6 payments of $950,000 each. To find the nominal quarterly compounded rate, we use the present value formula for annuities:$$PV = PMT \times \left(\frac{1 - (1 + r)^{-n}}{r}\right)$$Where:- $PV = \$5,250,000$ (present value of the lease liability),- $PMT = \$950,000$ (quarterly payment),- $n = 6$ (number of payments),- $r$ is the quarterly interest rate we need to find.Rearranging the formula to solve for $r$ involves trial and error or financial calculator functions. The correct rate that aligns the present value of the annuity (lease payments) with the liability recorded ($5,250,000) is found to be approximately 13.648%, which corresponds to choice E. This calculation typically requires the use of a financial calculator or spreadsheet software to solve for the rate that makes the present value of the annuity equal to the recorded liability.

Question 11

A lottery prize of $2,250,000 per year, payable at the beginning of every year for 20 years can also be collected as a single lump sum payment of $23,500,000. What effective annual rate was used in the calculation of this value?

Accepted Answer

The answer of A lottery prize of $2,250,000 per year,...

Question 12

Maria expects to have $750,000 in her retirement savings plan when she retires. From that, she plans to take out $4,500 at the beginning of every month for 30 years. What annual effective rate of interest will her money have to earn over the 30 years?

Accepted Answer

The scenario described is an example of an annuity due, where payments are made at the beginning of each period. To find the effective annual interest rate that allows Maria to withdraw $4,500 at the beginning of every month for 30 years from an initial amount of $750,000, we can use financial calculators or software designed for time value of money calculations. Given the complexity and the specific numbers involved, the calculation would typically involve solving for the interest rate that satisfies the equation for the present value of an annuity due. The correct answer, 6.225%, indicates the annual effective rate of interest required to meet Maria's retirement withdrawal goals.

Question 13

Determine the future value of the annuity due:

Accepted Answer