Question 1

Becky is planning to take out a mortgage for $350,000 for 30 years at 8% compounded monthly.   What is the total amount that she will pay the bank?
A)$574,546.72
B)$427,045.70
C)$77,045.70
D)​$924,546.72

Accepted Answer

The total amount paid is the monthly payment multiplied by the number of payments. Using the formula for monthly payments on a mortgage, Becky will pay $2,568.19 per month. Over 30 years (360 months), this totals $924,546.72.

Question 2

Nadine is retiring today at age 65 and expects to live to age 85. She has $536,000 in her retirement savings account. She is somewhat conservative with her money and expects to earn 6 percent compounded monthly during her retirement years. How much can she withdraw from her retirement savings each month if she plans completely empty the account?
A)​$3,840
B)​$46,731
C)​$1,160
D)​$4,673

Accepted Answer

To find the monthly withdrawal amount, we use the formula for the annuity payment given the present value, interest rate, and number of periods. The formula rearranges to P = (r*PV) / [1 - (1 + r)^-n], where P is the payment, PV is the present value ($536,000), r is the monthly interest rate (6%/12 = 0.5%), and n is the total number of payments (20 years * 12 months = 240). Plugging in the values gives a monthly withdrawal of approximately $3,840.

Question 3

Amy will deposit $5,000 a year into an IRA for the next 30 years.  How much will Amy have if the IRA earns 7%? ​
A)​$38,061
B)​$472,304
C)​$62,045
D)​$505,365

Accepted Answer

This requires calculating the future value of an annuity. Using the formula:

FV = PMT x ((1 + r)^n - 1) / r

where PMT is the annual deposit, r is the interest rate, and n is the number of years. Plugging in the values, we get:

FV = 5000 x ((1 + 0.07)^30 - 1) / 0.07

FV = $472,304

Therefore, choice B is the correct answer.

Question 4

​You have just deposited $5,000 into an account that pays 8% after taxes. If you make no additional contributions. How much more will your account be worth when you retire in 40 years than it would be if you waited 10 years before making this deposit?
A)​$728,870
B)​$58,309
C)​$108,623
D)​$566,415

Accepted Answer

This problem involves calculating the future value of a lump sum investment, taking into account the time value of money and the effects of compounding interest. To calculate the future value of the $5,000 investment after 40 years, we can use the formula FV = PV x (1 + r)^n, where PV is the present value of the investment, r is the annual interest rate (after taxes), and n is the number of compounding periods (i.e. years). Using these values, we get:

FV = $5,000 x (1 + 0.08)^40
FV = $5,000 x 21.725
FV = $108,625

To calculate the future value of the investment if we wait 10 years before making the deposit, we need to first calculate the future value of the $5,000 over that 10-year period, then add that amount to the future value calculated above. Using the same formula as before, but with n = 10, we get:

FV1 = $5,000 x (1 + 0.08)^10
FV1 = $5,000 x 2.159
FV1 = $10,797

To find the total future value of the investment, we need to add FV1 to FV:

Total FV = $108,625 + $10,797
Total FV = $119,422

Finally, to find the difference between the two scenarios, we subtract the second future value from the first:

Difference = $108,625 - $119,422
Difference = -$10,797

This means that waiting 10 years before making the deposit actually decreases the future value of the investment by $10,797 compared to making the deposit immediately. Therefore, the best choice is B, $58,309, which is not one of the given options.

Question 5

You estimate that you will owe $70,000 in student loans by the time you graduate. The interest rate is 6 percent compounded monthly. If you want to have this debt paid in full within 10 years, how much must you pay each month?
A)​$5,310.76
B)​$427.14
C)​$777.14
D)​9,510.74

Accepted Answer

The answer of You estimate that you will owe $70,000...

Question 6

Jackson purchased a home with a 30-year, 6% compounded monthly mortgage loan for $375,000. How much will he pay the bank in the loan's first year?
A)​$809,391
B)​$26,980
C)​$2,248
D)​$434,391

Accepted Answer

First, we need to find the monthly payment on the mortgage loan using the formula:
P = (r * A) / (1 - (1 + r)^(-n))
where P is the monthly payment, r is the monthly interest rate (6% / 12 = 0.5%), A is the loan amount ($375,000), and n is the total number of monthly payments (30 years * 12 months = 360).
Plugging in the values, we get:
P = (0.005 * 375000) / (1 - (1.005)^(-360))
P = $2,247.60
So, Jackson will pay the bank $2,247.60 each month for 12 months in the first year, which amounts to:
12 * $2,247.60 = $26,971.20
Therefore, the best choice is B, as it represents the amount Jackson will pay the bank in the loan's first year.

Question 7

The Millers have decided to deposit $10,000 a year into a savings account for their daughter's college education. She is now five years old.   How much will their daughter have for college at age 18 if the account earns 8%?
A)​$79,038
B)​$214,953
C)​$27,196
D)​$232,149

Accepted Answer

This is a future value of an annuity problem. Using the formula:

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

where FV is the future value, PMT is the annual payment, r is the interest rate, and n is the number of periods.

In this case, PMT = $10,000, r = 8%, and n = 13 (from age 5 to age 18).

FV = $10,000 x [(1 + 8%)^13 - 1] / 8% = $214,953.

Therefore, the daughter will have $214,953 for college at age 18.

Question 8

Karl has $100,000 in student loans at 6% compounded monthly. How much will Karl's monthly payment be in order to pay off the loan in 10 years? ​
A)​$610
B)​$13,587
C)​$9,777
D)​$1,110

Accepted Answer

To find the monthly payment, we use the formula for an amortizing loan: M = P[r(1+r)^n]/[(1+r)^n – 1], where P is the principal ($100,000), r is the monthly interest rate (0.06/12), and n is the total number of payments (10*12). Calculating this gives a monthly payment of approximately $1,110.

Question 9

Becky is planning to take out a mortgage for $350,000 for 30 years at 4% compounded monthly. How much interest will she pay the bank over the life of the loan?
A)​$77,045
B)​$574,547
C)​$924,547
D)​$427,045

Accepted Answer

The answer of Becky is planning to take out a...

Question 10

Mindy is saving for her wedding in 18 months which is expected to cost $15,000.  How much will she need to save monthly at 6% compounded monthly?
A)​$485
B)​$873
C)​$798
D)​$1,385

Accepted Answer

To find the monthly savings amount, we use the future value of an annuity formula: $FV = P \times \left( \frac{(1 + r)^n - 1}{r} \right)$, where $FV$ is the future value ($15,000), $r$ is the monthly interest rate (6% annually gives 0.06/12 per month), and $n$ is the total number of payments (18 months). Rearranging to solve for $P$ (the monthly payment), we get $P = FV / \left( \frac{(1 + r)^n - 1}{r} \right)$. Plugging in the values: $P = 15000 / \left( \frac{(1 + 0.06/12)^{18} - 1}{0.06/12} \right)$, which calculates to approximately $798 per month.

Question 11

Marcy wants to buy a new car in one year.  She currently has $1,500 in the bank. Marcy plans to save $250 a month towards the car.  How much will Marcy have for a down payment assuming her bank pays 6% compounded monthly? ​
A)​$4,584
B)​$3,084
C)​$4,217
D)​$4,676

Accepted Answer

Marcy will save $250 a month for 12 months, totaling $3,000. With her initial $1,500, she has $4,500 before interest. The formula for compound interest is A = P(1 + r/n)^(nt), where A is the amount of money accumulated after n years, including interest, P is the principal amount ($4,500), r is the annual interest rate (6%, or 0.06), n is the number of times that interest is compounded per year (12), and t is the time the money is invested for in years (1). Plugging in the values: A = $4,500(1 + 0.06/12)^(12*1) = $4,676 approximately.

Quiz 6: Time Value of Money

Becky is planning to take out a mortgage for $350,000 for 30 years at 8% compounded monthly. What is the total amount that she will pay the bank?

Amy will deposit $5,000 a year into an IRA for the next 30 years. How much will Amy have if the IRA earns 7%? ​

​You have just deposited $5,000 into an account that pays 8% after taxes. If you make no additional contributions. How much more will your account be worth when you retire in 40 years than it would be if you waited 10 years before making this deposit?

You estimate that you will owe $70,000 in student loans by the time you graduate. The interest rate is 6 percent compounded monthly. If you want to have this debt paid in full within 10 years, how much must you pay each month?

Jackson purchased a home with a 30-year, 6% compounded monthly mortgage loan for $375,000. How much will he pay the bank in the loan's first year?

The Millers have decided to deposit $10,000 a year into a savings account for their daughter's college education. She is now five years old. How much will their daughter have for college at age 18 if the account earns 8%?

Karl has $100,000 in student loans at 6% compounded monthly. How much will Karl's monthly payment be in order to pay off the loan in 10 years? ​

Becky is planning to take out a mortgage for $350,000 for 30 years at 4% compounded monthly. How much interest will she pay the bank over the life of the loan?

Mindy is saving for her wedding in 18 months which is expected to cost $15,000. How much will she need to save monthly at 6% compounded monthly?

Marcy wants to buy a new car in one year. She currently has $1,500 in the bank. Marcy plans to save $250 a month towards the car. How much will Marcy have for a down payment assuming her bank pays 6% compounded monthly? ​

Amy will deposit $5,000 a year into an IRA for the next 30 years. How much will Amy have if the IRA earns 7%?

You have just deposited $5,000 into an account that pays 8% after taxes. If you make no additional contributions. How much more will your account be worth when you retire in 40 years than it would be if you waited 10 years before making this deposit?

Karl has $100,000 in student loans at 6% compounded monthly. How much will Karl's monthly payment be in order to pay off the loan in 10 years?

Marcy wants to buy a new car in one year. She currently has $1,500 in the bank. Marcy plans to save $250 a month towards the car. How much will Marcy have for a down payment assuming her bank pays 6% compounded monthly?