Compound Interest and Present Value

Present value is the opposite of (blank) value; it brings the value back to today instead of extending it out into the future

future

compounding is when interest is earned on:

the principal and prior periods' interest

Match the number of times interest is paid each year with the compounding term

1-annual 2- semiannual 4- quarterly 12- monthly 360- daily

Given principle of $100 and rate of 10%, match the number of years to the amount of interest earned using simple interest. 1. 1 year 2. 2 years 3. 3 years A. $20 B. $30 C. $10

1. = C 2. = A. 3. = B.

Order the steps in calculating the compound amount and interest manually.

1. Calculate the simple interest and add it to the principal. Use this total for the next year 2. Repeat the calculation of the simple interest plus the principal for the total number of periods 3. Compound amount- Principal= Compound Interest

Order the steps in calculating present value

1. Find the number of period n: Years multiplied by number of time interest is compounded in one year.. 2. Find the rate i: Annual rate divided by number of times interest is compounded in one year. 3. Plug the FV amount, n and i into the PV formula. 4. Solve by using the PV formula

Order the steps for calculating the compound amount using the formula

1. Find the number of periods n. Years multplied by the number of times interest is compounded in 1 year. 2. Find the rate i. Annual rate divided by number of times interest is compounded in 1 year. 3. Plug the PV amount, n and i, into the following formula: FV=PV(1+i)^n.

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

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

You compound $1 for 3 years at 4% interest. Match the number of periods to the resective compounding periods

3- Annual (Annual= 1 times per year x number of years of 3; 1*3= 3 periods) 6- Semiannual ( Semiannual= 2 times per year x 3 years = 6 periods) 12- Quarterly (Quarterly= 4 times per year x 3 years= 12 periods) 36- Monthly ( Monthly= 12 times per year x 3 years = 38 periods)

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

6

The future value formula is (Blank) times ( 1+i)^n while the present value formula is (Blank) divided by (1+i)^n

PV, FV

Which of these is a true statement about APY versus the nominal rate of interest?

The APY will be higher than the nominal rate because of the compounding of interest

When using a financial calculator, the keystrokes for PV are identical except for the answer being sought (solve for PV or solve for FV); this shows that:

The FV formula can be used to check PV calculations, and vice versa.

Which of these is a true statement about compounding of interest?

The more often you compound, the more interest that will be earned on the principal.

True or False: Present value is the concept that money received in the future is not worth as much today )the present).

True

True or False: You can use the present value formula to check your work by reversing the future value formula.

True

When you are looking for compounded about (both principal and interest), you are searching for (blank) (blank)

future value

Compound interest results in (Blank) interest over time than simple interest.

greater

Given the equation, FV=PV(1+i)^N, Match the abbreviation to the respective compounding term

i- Rate per Period FV- Compound Amount N- Number of Periods PV- Principal

Using the PV formula, i refers to the interest rate per period: the annual (blank) divided by the number of compounding period per (blank)

rate, year

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

today

Cheng deposited $800 in a savings account for 4 years with a 6% annual compounding rate. Match the compounding year to the interest earned.

Year 1- 48.00 ( $800*.06*= $48) Year 2- $50.88 ( $800* .06* 1= $48. $800+ $48 = $848. $848* .06= $50.88) Year 3- 53.93 ( $800* .06* 1= $48. $800 + $48= $848. $848* .06= $50.88. $848+ $50.88= $898.88. $898.88* .06= $53.93)

Money today is less risky than money you will receive in the future. Why is this so?

- Purchasing power decreases over time so your money is worth less if prices rise faster than your interest rate - Default risk (the borrower may not repay as agreed)

You compound $1 for 3 years at 12% interest. Match the interest rate for each period to the respective compounding periods.

1%- Monthly (12%/ 12 months= 1% per period) 3%- Quarterly (12%/ 4 times per year= 3% per period) 6%- Semiannual (12%/2 times per year= 6% per period) 12%- Annual (12%/ 1 times per year= 12% per period)

$1 is compounded annually for 3 years at 24% interest. What is the interest rate per period?

24% 24%/ 1=24%

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

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

Present value starts with what an item is worth in the (blank) and calculates what that item is worth in the (blank)

Future, present PV starts with what an item is worth in the future and calculates what that item is worth in the present.

Using present value would answer which of the following questions?

How much money do I need today to meet a need in the future?