Section 6.1 Compound

Simple Interest Formulas:

Interest: I = P rt

Accumulated amount: A = P (1 + rt)

Here P is the principal (money you start out with), r is the (as a decimal), and t is the time (in years).

1. Find the accumulated amount at the end of 9 months on a $1800 bank deposit paying simple interest at a rate of 9%/year. (Round answer to the nearest cent.)

2. A bank deposit paying simple interest at the rate of 6%/year grew to a sum of $1300 in 8 months. Find the principal. (Round answer to the nearest cent.) 3. Determine the simple interest rate at which $2400 will grow to $2495 in 5 months. (Round answer to two decimal places.)

4. Determine the time needed for $2600 to grow to $3000 with simple interest paid at a rate at 5.6%/year. (Round answer to the nearest year.)

5. Find the interest earned on a $2200 bank deposit paying simple interest at a rate of 8.5%/year after 11 months. (Round answer to the nearest cent.)

2 Fall 2019, © Maya Johnson Compounded Interest Formulas: Accumulated Amount

A = P (1 + i)n

r where i = m , n = mt, and

A = Accumulated amount at the end of n conversion periods. P = Principal. r = Nominal interest rate per year. m = Number of conversion periods per year. t = Term (number of years)

Calculator Functions

TVM Solver: We can use the TVM Solver on our calculator to solve problems involving com- pound interest. To access the Menu, you need to press APPS , 1 , and then 1 again. (Please note that if you have a plain TI-83, you need to press 2ND , x−1 to access the Finance Menu). Below we define the inputs on the TVM Solver:

N = mt =the total number of compounding periods I% = interest rate (as a percentage) PV = (principal amount). Entered as a negative number if invested, a positive number if borrowed. PMT = payment amount FV = (accummulated amount) P/Y = C/Y = m =the number of compounding periods per year.

Move the cursor to the value you are solving for and hit ALPHA and then ENTER.

6. Find the present value of $40, 000 due in 4 years at the given rate of interest. (Round answer to the nearest cent.) 10%/year compounded daily.

N = I% = PV = PMT = FV = P/Y = C/Y =

3 Fall 2019, © Maya Johnson 7. A young man is the beneficiary of a trust fund established for him 16 years ago at his birth. If the original amount placed in trust was $20, 000, how much will he receive if the money has earned interest at the rate of 9%/year compounded quarterly? (Round answer to the nearest cent.)

N = I% = PV = PMT = FV = P/Y = C/Y =

8. Five and a half years ago, Chris invested $10, 000 in a retirement fund that grew at the rate of 10.82%/year compounded quarterly. What is his account worth today? (Round answer to the nearest cent.)

N = I% = PV = PMT = FV = P/Y = C/Y =

9. Kim invested a sum of money 7 years ago in a savings account that has since paid interest at the rate of 8.5%/year compounded monthly. Her investment is now worth $36, 184.65. How much did she originally invest? (Round answer to the nearest cent.)

N = I% = PV = PMT = FV = P/Y = C/Y =

4 Fall 2019, © Maya Johnson 10. Your rich uncle has just given you a high school graduation present of $1, 400, 000. The present, however, is in the form of an 18-year bond with an annual interest rate of 4.7% compounded annually. The bond says that it will be worth $1, 400, 000 in 18 years. What is this gift worth at the present time? (Round answer to the nearest cent.)

N = I% = PV = PMT = FV = P/Y = C/Y =

Effective Rate of Interest Formula:

 r m r = 1 + − 1 eff m

Calculator Steps:

Press APPS , 1 , scroll down to Eff and hit ENTER . The format is Eff(annual interest rate as a percentage, the number of compounding periods per year)

5 Fall 2019, © Maya Johnson 11. Find the effective rate of interest corresponding to a nominal rate of 11.5%/year compounded in the following ways. (Round answers to two decimal places.)

(a) compounded annually

(b) compounded semiannually

(c) Which interest rate would you prefer if you were earning the interest through a savings account? Which one would you choose if you were paying the interest through a bank ?

6 Fall 2019, © Maya Johnson