Question 1

If you save $350 per month in an account paying 2.75% interest compounded monthly, how much will you have in that account 12 years later?

Accepted Answer

We can use the formula for compound interest to solve this problem:

FV = PV(1+r/n)^(nt)

Where:
FV = future value (what we want to find)
PV = present value (how much we start with, in this case $0)
r = annual interest rate (2.75%)
n = number of times interest is compounded per year (12 for monthly)
t = time in years (12)

Plugging in these values, we get:

FV = 0(1+0.0275/12)^(12*12) + (350*(((1+0.0275/12)^(12*12)-1)/(0.0275/12)))
FV ≈ $59,631.31

Therefore, the best choice is C, which is closest to our calculated answer.

Question 2

A computer was purchased in 1996 for $2500. Its value in current dollars depreciates steadily at a rate of 30% per year. What will the computer's value be at the beginning of 2003?

Accepted Answer

The value of the computer depreciates by 30% each year, meaning it retains 70% of its value annually. The number of years from 1996 to 2003 is 7 years. The value in 2003 is calculated as $2500 * (0.7)^7 = $205.89.

Question 3

Suppose that you have $4000 on deposit at your bank at an annual rate of 1.5%. If the bank compounds continuously, how much interest do you receive after three years?

Accepted Answer

We can use the formula for continuous compounding:

A = Pe^(rt)

where A is the final amount, P is the initial principal, e is the base of the natural logarithm, r is the annual interest rate (as a decimal), and t is the time in years.

In this case, we have P = 4000, r = 0.015, and t = 3. Plugging in these values, we get:

A = 4000*e^(0.015*3) ≈ 4374.11

So the interest earned is:

Interest = A - P ≈ 4374.11 - 4000 ≈ $374.11

Rounding this to the nearest cent, we get:

Interest ≈ $184.11

Therefore, the best choice is D.

Question 4

Suppose that you have $2000 on deposit at your bank at an annual rate of 2.34%. If the bank compounds continuously, what is the balance of your account after two years?

Accepted Answer

The answer of Suppose that you have $2000 on deposit...

Question 5

Betty bought a house in 1987 for $99,000 and sold it in 2014. If the 1987 CPI is 113.6 and the 2014 CPI is 236.7, how much would the house be worth in 2014 dollars?

Accepted Answer

To adjust the 1987 price to 2014 dollars, you use the formula: (Price in 1987 dollars) * (2014 CPI / 1987 CPI) = Price in 2014 dollars. Plugging in the numbers: $99,000 * (236.7 / 113.6) = $206,279.

Question 6

In early 2002, the inflation rate was about 1.4%. If you invested in a savings account with an annual interest rate of 4.8%, what was the real growth rate of this investment?

Accepted Answer

The real growth rate can be calculated by subtracting the inflation rate from the interest rate.

Real growth rate = 4.8% - 1.4% = 3.4%

Therefore, the correct answer is B (3.35%).

Question 7

A computer was purchased in 1999 for $3000. Its value in current dollars depreciates steadily at a rate of 25% per year. What will the computer's value be at the beginning of 2003?

Accepted Answer

To find the value of the computer at the beginning of 2003, we need to apply the depreciation rate of 25% per year for the years 1999 to 2002 (4 years). 
So, the value of the computer at the beginning of 2003 can be found as: 
$3000 * (1-0.25)^4 = $949.22 
Therefore, the answer is choice B.

Question 8

Javier bought a house in 1974 for $49,000 and sold it in 2014. If the 1974 CPI is 49.3 and the 1997 CPI is 160.5, how much would the house be worth in 2014 dollars?

Accepted Answer

To adjust the 1974 price to 2014 dollars, we use the formula: Adjusted Price = Original Price * (CPI in 2014 / CPI in 1974). Given the CPI in 1974 is 49.3 and the CPI in 1997 is 160.5, we first need the CPI for 2014, which isn't directly provided. However, assuming a mistake in the question and that it meant to use the 1997 CPI as a reference for adjustment (since the 2014 CPI isn't given), we adjust the 1974 price to 1997 dollars first: $49,000 * (160.5 / 49.3) = $160,500. This calculation, however, directly leads to none of the provided answers, suggesting a misunderstanding in the question's intent or a need for additional information (like the 2014 CPI) for accurate calculation. Given the options and assuming a direct calculation mistake, the closest answer by approximation and considering typical inflation trends would be A) $235,260, assuming the house's value increased in line with general inflation trends over the period from 1974 to 2014.

Question 9

Use the geometric series formula to find the sum of 1 - q + q² - q³ + q⁴.

Accepted Answer

The series is a geometric series with the first term $a = 1$ and common ratio $r = -q$. The sum of the first $n$ terms of a geometric series is given by $S_n = \frac{a(r^n - 1)}{r - 1}$. Here, $n = 5$, so the sum is $\frac{1((-q)^5 - 1)}{-q - 1}$.

Question 10

A car was purchased in 1980 for $12,000. Its value in current dollars depreciates steadily at a rate of 14% per year. What will the car's value be at the beginning of 2003?

Accepted Answer

The car's value depreciates by 14% each year, so its value each year is 86% of the previous year's value. From 1980 to 2003 is 23 years. The value in 2003 is $12,000 * (0.86)^23, which equals approximately $373.81.

Question 11

A man makes $10 deposits each quarter into a savings account earning 8% interest compounded quarterly. He continues these deposits for 12 years. How much will the account be worth after 12 years?

Accepted Answer

The answer of A man makes $10 deposits each quarter...

Question 12

Use the geometric series formula to find the sum of of  $1 + \frac { 1 } { 4 } + \frac { 1 } { 4 ^ { 2 } } + \frac { 1 } { 4 ^ { 3 } } + \frac { 1 } { 4 ^ { 4 } }$

Accepted Answer

The sum of a geometric series is given by $S = \frac{a(1 - r^n)}{1 - r}$, where $a$ is the first term, $r$ is the common ratio, and $n$ is the number of terms. Here, $a = 1$, $r = \frac{1}{4}$, and $n = 5$. Substituting these values into the formula gives $S = \frac{1(1 - (\frac{1}{4})^5)}{1 - \frac{1}{4}}$, which simplifies to the expression in choice B.

Question 13

John bought a house in 1947 for $19,000 and sold it in 1997. If the 1947 CPI is 22.3 and the 2014 CPI is 236.7, how much would the house be worth in 2014 dollars?

Accepted Answer

To adjust the 1947 price to 2014 dollars, use the formula: (2014 CPI / 1947 CPI) * 1947 price. Plugging in the values: (236.7 / 22.3) * $19,000 = $201,673.

Question 14

If the rate of a 24-month CD is 1.15% compounded daily, how much would need to be set aside in such a CD to have $25,000 at the end of 24-month term?

Accepted Answer

Using the formula for compound interest, we can solve for the amount needed to be invested:
A = P(1 + r/n)^(nt)
Where:
A = amount at the end of 24 months = $25,000
P = principal (what we want to solve for)
r = annual interest rate = 1.15%
n = number of times compounded per year = 365 (since interest is compounded daily)
t = time in years = 2 (since 24 months is 2 years)

Plugging in these values, we get:
$25,000 = P(1 + 0.0115/365)^(365*2)
Simplifying and solving for P, we get:
P = $24,431.57

Therefore, the best choice is B.

Question 15

In late 2001 the inflation rate was about 2.9%. If you invested in a savings account with an annual interest rate of 9.2%, what was the real growth rate of this investment?

Accepted Answer

First, we need to calculate the real interest rate using the formula:
real interest rate = nominal interest rate - inflation rate
real interest rate = 9.2% - 2.9% 
real interest rate = 6.3%
Then, we can use the formula for real growth rate which includes the real interest rate:
real growth rate = (1 + nominal interest rate) / (1 + inflation rate) - 1
real growth rate = (1 + 9.2%) / (1 + 2.9%) - 1
real growth rate = 6.12%
Therefore, the real growth rate of this investment was 6.12%, which is option D.

Question 16

Use the geometric series formula to find the sum of  1 – 2 + 4 – 8 + 16.

Accepted Answer

The given series can be written as:

1 - 2 + 4 - 8 + 16 = 1 + (-2) + 4 + (-8) + 16

This is an alternating series with common ratio r = -2.

Using the formula for the sum of an alternating geometric series, we have:

S = a / (1 - r)

where a is the first term of the series.

In this case, a = 1 and r = -2, so:

S = 1 / (1 - (-2)) = 1 / 3

Therefore, the sum of the series 1 - 2 + 4 - 8 + 16 is:

1 - 2 + 4 - 8 + 16 = S = 1/3

The only answer choice that matches this result is C.

Question 17

A car was purchased in 1985 for $15,000. Its value in current dollars depreciates steadily at a rate of 13% per year. What will the car's value be at the beginning of 2003?

Accepted Answer

The answer of A car was purchased in 1985 for...

Question 18

The Chavez family has decided to save up for a new spa. They want to save $10,000 in five years. They find a savings account for which interest was compounded monthly at 8.2%. How much will they have to deposit each month to meet this goal?

Accepted Answer

We can use the formula for future value of an annuity to calculate the monthly deposit needed.

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

Where:
FV = future value (which is $10,000 in this case)
PMT = monthly deposit we need to find
r = annual interest rate (8.2%)
n = number of times interest is compounded per year (12 for monthly)
t = number of years (5)

Plugging in the values, we get:

10,000 = PMT * [(1 + 0.082/12)^(12*5) - 1]/(0.082/12)

Solving for PMT gives us:

PMT = 135.14

Rounding up to the nearest dollar, the monthly deposit needed is $135. Therefore, the best choice is (C).

Question 19

Use the geometric series formula to find the sum of $\ {a}+ {a^2} + {a^3} + {a^4}$ [Hint: The series does not begin with 1.]

Accepted Answer

The answer of Use the geometric series formula to find...

Question 20

Buck bought a house in 1967 for $19,000 and sold it in 2001. If the 1967 CPI is 33.4 and the 2014 CPI is 236.7, how much would the house be worth in 2014 dollars?

Accepted Answer

The answer of Buck bought a house in 1967 for...

Quiz 21: Savings Models