GENMATH REMEDIAL 2ND QUARTER

Which of the following is the formula for calculating simple interest?

• I = P + r + t

• I = P * (1 + r) * t

• I = P / r / t

• I = P * r * t

Answer explanation

The formula for calculating simple interest is I = P * r * t, where I is the interest, P is the principal amount, r is the rate of interest, and t is the time period. This formula correctly represents how interest accumulates.

What is the key difference between simple and compound interest?

• Compound interest is calculated only on the principal amount.

• The key difference is that simple interest is calculated only on the principal, whereas compound interest is calculated on the principal plus accumulated interest.

• Simple interest is always higher than compound interest.

• Simple interest can be compounded over time.

Answer explanation

The key difference is that simple interest is calculated only on the principal amount, while compound interest is calculated on the principal plus any accumulated interest, leading to potentially higher returns over time.

Which of the following best describes compound interest?

• A fixed percentage of the principal paid annually.

• Interest that does not change over time.

• Interest calculated on both the initial principal and the accumulated interest.

• Interest calculated only on the initial principal.

Answer explanation

Compound interest is calculated on both the initial principal and the accumulated interest, meaning that interest earns interest over time, unlike simple interest which is only on the principal.

What is the formula for compound interest?

• A = P (1 + r)^(nt)

• A = P (1 + r/n)^(nt)

• A = P e^(rt)

• A = P (1 - r/n)^(nt)

Answer explanation

The correct formula for compound interest is A = P (1 + r/n)^(nt), where A is the amount, P is the principal, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the time in years.

What is the term used to describe the final amount after interest is applied?

• Principal Amount

• Future Value

• Present Value

• Net Worth

Answer explanation

The term 'Future Value' refers to the total amount of money that will be accumulated after interest is applied to the principal amount over a specified period. It represents the value of an investment at a future date.

How is the maturity value of an investment with compound interest calculated?

• M = P(1 + r)^(nt)

• M = P(1 + r/n)^(nt)

• M = P(1 + r/n)^t

• M = P(1 + n/r)^(nt)

Answer explanation

The maturity value M of an investment with compound interest is calculated using the formula M = P(1 + r/n)^(nt), where P is the principal, r is the annual interest rate, n is the number of compounding periods per year, and t is the number of years.

If an investment of $1,000 is made at an interest rate of 5% for 3 years, with interest compounded annually, what is the future value?

• 1050.75

• 1200.00

• 1100.50

• 1157.63

Answer explanation

To find the future value, use the formula FV = P(1 + r)^n. Here, P = 1000, r = 0.05, and n = 3. Thus, FV = 1000(1 + 0.05)^3 = 1000(1.157625) = 1157.63. Therefore, the correct answer is 1157.63.

What does "compounding frequency" refer to in compound interest?

• The initial amount of money before any interest is applied.

• The rate at which the principal amount increases over time.

• The number of times interest is calculated and added to the principal in a given period.

• The total amount of money accumulated after a certain period.

Answer explanation

Compounding frequency refers to how often interest is calculated and added to the principal. The correct choice highlights that it is the number of times this occurs in a specific period, impacting the total interest earned.

Which of the following is true about the relationship between time and compound interest?

• Compound interest decreases over time.

• Time has no effect on compound interest.

• The longer the time, the greater the compound interest.

• Shorter time periods yield higher compound interest.

Answer explanation

The longer the time, the greater the compound interest, as interest is calculated on the accumulated amount over time, leading to exponential growth. Thus, more time results in more interest earned.

If $500 is invested at an interest rate of 6% per year, compounded annually for 4 years, what will be the maturity value?

• 631.24

• 500.00

• 600.00

• 700.00

Answer explanation

The maturity value is calculated using the formula A = P(1 + r)^t. Here, P = 500, r = 0.06, and t = 4. Thus, A = 500(1 + 0.06)^4 = 631.24. Therefore, the correct answer is 631.24.