Business Math: CH12 -Compound Interest and Present Value

When interest is compounded semiannually, interest is calculated how many times per year? A) 3 B) 2 C) 4 D) 6

Semiannual calculates interest twice per year.

$1 is compounded semiannually for 5 years at 2% interest. How many periods will this result in?

Semiannual compounding results in twice a year. Therefore, 2 × 5 years = 10 periods.

Present value answers the question, "How much do I need to invest ______________ for it to grow to $1 in the future?

TODAY

Determine the effective rate of $1 invested at 6% compounded semiannually. A) 6.09% B) 3% C) 6%

Table value of 1.0609 × $1 = Maturity Value of $1.0609. Subtract the Principal to find the interest of $.0609. Interest for one year of $.0609 ÷ Principal of 1 = 6.09% is the effective or actual rate, also known as the annual percentage yield.

Compound interest results in _______________ interest over time than simple interest.

higher or Greater

Jose invested $50,000 at 12% for 4 years compounded annually. What is the maturity value at the end of Year 3? A) $56,000 B) $78,675.97 C) $70,246.40 D) $62,720

$50,000 (1 + .12)3 = $50,000 $50,000 (1.404928) = $70,246.40 maturity value at the end of Year 3.

$1 is compounded annually for 3 years at 24% interest. What is the interest rate per period? A) 6% B) 24% C) 12% D) 8%

24% ÷ 1 = 24%.

Using the Rule of 72, how many years will it take to double your investment at 12% per year?

72 ÷ 12 = 6 years

Using the Rule of 72, how many years will it take to double your investment at 12% per year? A) 8.64 B) 600 C) 6

72 ÷ 12 = 6 years

$1 is compounded semiannually for 10 years at 8% interest. What is the interest rate per period? A) 2% B) 8% C) 1% D) 4%

8% ÷ 2 (semiannual) = 4%.

What is the equation to calculate compound interest?

Principle x Table Factor

You compound $1 for 3 years at 12% interest. Match the interest rate for each period to the respective compounding periods. A) 1% B) 3% C) 6% D) 12%

A) 1% -- Monthly B) 3% -- Quarterly C) 6% -- Semiannual D) 12% -- Annual

You compound $1 for 3 years at 4% interest. Match the number of periods to the respective compounding periods. A) 3 B) 6 C) 12 D) 36

A) 3 -- Annual B) 6 -- Semiannual C) 12 -- Quarterly D) 36 -- Monthly

Cheng deposited $800 in a savings account for 4 years with a 6% annual compounding rate. Match the compounding year to the interest earned. A) Year 1 B) Year 2 C) Year 3

A) Year 1 -- $48.00 B) Year 2 -- $50.88 C) Year 3 -- $53.93

Compounding is when interest is earned on: A) the principal and prior periods' interest B) the prior periods' interest C) the principal

A) the principal and prior periods' interest

Consider which option results in a higher effective rate. Bank A offers 4% compounded annually. Bank B offers 4% compounded quarterly. A) Bank A B) Bank B

B) Bank B Bank B's effective rate is 4.06%. 4% quarterly pays 1% four times per year. 1^4 = 4.06%. Bank A's effective rate is 4%. 4^1 = 4%.

Compounding looks at what $1 today will be in the __________. A) past B) future C) present

B) future

Compounding goes from (present/future)______________ value to (present/future)______________

Compounding goes from present value to future value.

True or false: The APY (annual percentage yield) is different from the effective rate.

False

The number of periods for a table lookup on $5,000 at 12% compounded semiannually for 10 years is 10 periods.

False 20 Periods

True or false: The APY (annual percentage yield) is different from the effective rate.

False. Banks use the APY and the effective rate interchangeably.

Present value starts with what an item is worth in the __________ and calculates what that item is worth in the __________.

Future; Present

What is the equation to calculate Effective Rate (AKA Annual Percentage Yield)?

Interest for 1 year/Principal = APY

Present value table factors are numbers (more/less) than 1.

Less

Wright invested $500 at 7% compounded daily for 6 years. What is the future value of his investment? A) $760.95 B) $536.25 C) $750.35

N = 6; i = 7%. $500 × 1.5219 = $760.95. Use the compounded daily table.

What is the equation to calculate simple interest?

Principal x Rate x Time

Feliz borrowed $2,000 for 5 years at 6%. Using the simple interest formula, how much will he need to pay at the end of the loan? A) $2,600 B) $120 C) $2,000 D) $600

The maturity value is the principal plus the interest. $2,000 × 6% × 5 years= $600 + $2,000 = $2,600

True or false: You can use the present value tables to check your work by reversing the future value table

True Once you find the present value of a future number, you can use the future value table to extend the present value figure into the future.

The _________________________ law forced savings institutions to reveal their actual rate of interest.

Truth in Savings