Question 1

_______________ interest is calculated by applying the interest rate to the principal only, not to interest earned.

Accepted Answer

Simple interest is calculated by multiplying the principal by the interest rate and the time period. It does not take into account the interest earned over time, only the original principal.

Question 2

Assume a 30-month CD purchased for $2500 pays simple interest at an annual rate of 6%. What is the balance at maturity?

Accepted Answer

The interest earned on the CD can be calculated using the formula for simple interest: I = PRT, where P is the principal amount ($2500), R is the annual interest rate (6% or 0.06), and T is the time in years (30 months or 2.5 years). Thus, I = $2500 * 0.06 * 2.5 = $375. The total balance at maturity is the sum of the principal and the interest earned, which is $2500 + $375 = $2875.

Question 3

We can afford to make payments of $350 per month for four years. What is the largest amount of a loan we can get at an APR of 5%?

Accepted Answer

To find the largest loan amount, we use the formula for the present value of an annuity. The monthly interest rate is 5%/12, and the number of payments is 4*12. Using these values, the largest loan amount is approximately $15,198.

Question 4

The _______________ of an investment is the value of that investment at some specified time in the future.

Accepted Answer

The future value of an investment is the expected value of that investment at some specified time in the future. It takes into account factors such as the initial investment amount, the interest or growth rate, and the time horizon.

Question 5

If interest is compounded 12 times per year, the period interest rate is .

Accepted Answer

The answer of If interest is compounded 12 times per...

Question 6

At age 25, you start work for a company that deposits $10,000 into a retirement account that pays a monthly interest rate of 1.1%, and interest is compounded monthly. If you retire at 65, what is the balance in this account?

Accepted Answer

The correct answer is A because the balance in the account at age 65 is $1,907,895.94. This is calculated using the formula A = P(1 + r/n)^(nt), where A is the future value of the investment, P is the principal investment, r is the annual interest rate, n is the number of times per year that interest is compounded, and t is the number of years. In this case, P = $10,000, r = 1.1%, n = 12, and t = 40. Plugging these values into the formula, we get A = $1,907,895.94.

Question 7

Consider a savings account paying an APR of 4% compounded semi-annually. Compare the doubling time using the Rule of 72 with the exact doubling time.

Accepted Answer

The answer of Consider a savings account paying an APR...

Question 8

If you borrow money to pay for an item, your _______________ in that item at a given time is the part of the principal you have paid.

Accepted Answer

Equity refers to the portion of an asset that you own outright, which is calculated by subtracting the amount of borrowed funds (the principal) from the current market value of the asset. Amortization refers to the process of paying off a loan over time through regular payments of both principal and interest, while investment and interest do not accurately describe the concept of ownership in an item purchased with borrowed funds.

Question 9

Suppose you have invested $1500 at an APR of 8%. Use the Rule of 72 to estimate how long it will be until your investment reaches $3000.

Accepted Answer

The answer of Suppose you have invested $1500 at an...

Question 10

The Rule of 72 states that the estimate for doubling time = _______________ .

Accepted Answer

The answer of The Rule of 72 states that the...

Question 11

The largest monthly payment we can afford is $360. Can we afford to borrow a principal of $6750 with a term of 18 months?

Accepted Answer

To determine if the monthly payment is affordable, divide the total principal by the number of months: $6750 / 18 months = $375 per month, which exceeds the affordable $360 monthly payment. Interest is not mentioned, so this calculation assumes no interest.

Question 12

What is the future value of a 5-year investment of $3000 at an APR of 7% compounded monthly?

Accepted Answer

Using the formula for compound interest, we get:
Future Value = P(1+(r/n))^(nt)
Where:
P = principal amount (initial investment) = $3000
r = annual interest rate = 7% = 0.07
n = number of times the interest is compounded per year = 12 (monthly)
t = time the money is invested (in years) = 5

Plugging in the values, we get:
Future Value = 3000(1+(0.07/12))^(12*5)
= $4252.88

Question 13

As an investor, you are searching for the highest possible rate. Which of the following options gives the highest APY?

Accepted Answer

The APY (Annual Percentage Yield) can be calculated using the formula APY = (1 + r/n)^(n*p) - 1, where r is the annual interest rate (APR), n is the number of compounding periods per year, and p is the number of years. For a one-year period, the formula simplifies to APY = (1 + r/n)^n - 1. Compounding more frequently at the same APR results in a higher APY, but since all the APRs are different, we need to calculate each option's APY to compare. Option A, with an APR of 3.25% compounded semiannually, results in the highest APY compared to the other options with lower APRs, even though they compound more frequently.

Question 14

The going rate for a home mortgage with a term of 30 years is 6%. The lending agency says that based on your income, your monthly payment can be at most $900. How much can you borrow?

Accepted Answer

The answer of The going rate for a home mortgage...

Question 15

Suppose you invest $5000 in a savings account that pays an APR of 4%. If the interest is compounded monthly, what is the balance in the account after 10 years?

Accepted Answer

The answer of Suppose you invest $5000 in a savings...

Question 16

To buy a car, you borrow $25,000 with a term of three years at an APR of 6.5%. What is your monthly payment?

Accepted Answer

To calculate the monthly payment, we can use the formula:

M = P * (r(1+r)^n) / ((1+r)^n - 1)

where:
M = monthly payment
P = principal (amount borrowed) = $25,000
r = monthly interest rate = APR / 12 = 6.5% / 12 = 0.0054167
n = total number of payments = 3 years * 12 months/year = 36

Plugging in the values, we get:

M = $25,000 * (0.0054167*(1+0.0054167)^36) / ((1+0.0054167)^36 - 1) = $766.23 (rounded to the nearest cent)

Therefore, the monthly payment is $766.23, which corresponds to choice B.

Question 17

Assume a six-month CD purchased for $5000 pays simple interest at an annual rate of 9.5%. How much interest does it earn?

Accepted Answer

The interest earned on a CD can be calculated using the formula I = PRT, where I is the interest, P is the principal amount ($5000), R is the annual interest rate (9.5% or 0.095), and T is the time in years (0.5 years for six months). Thus, I = $5000 * 0.095 * 0.5 = $237.50.

Question 18

What is the present value of an investment that will be worth $5000 at the end of ten years assuming an APR of 8% compounded monthly?

Accepted Answer

The answer of What is the present value of an...

Question 19

A fairly good estimate for a long-term loan with a moderate or high interest rate is that the monthly payment is _______________ as large as the principal times the monthly interest rate.

Accepted Answer

For a long-term loan with a moderate or high interest rate, the monthly payment needs to cover not only the interest but also a portion of the principal. Therefore, it is at least as large as the principal times the monthly interest rate, to ensure both interest and principal are being paid down over time.

Question 20

Joe bought a nine-month CD for $1500. He said that at maturity it paid $82.13 in simple interest. Compute the corresponding yearly interest rate.

Accepted Answer

The answer of Joe bought a nine-month CD for $1500....

Quiz 4: Personal Finance