Question

Find the amount to which $300 will grow under each of these conditions:

1. 4% compounded annually for 6 years. Do not round intermediate calculations. Round your answer to the nearest cent.

2. 4% compounded semiannually for 6 years. Do not round intermediate calculations. Round your answer to the nearest cent.

   $  

3. 4% compounded quarterly for 6 years. Do not round intermediate calculations. Round your answer to the nearest cent.

   $  

4. 4% compounded monthly for 6 years. Do not round intermediate calculations. Round your answer to the nearest cent.

   $  

5. 4% compounded daily for 6 years. Assume 365-days in a year. Do not round intermediate calculations. Round your answer to the nearest cent.

   $  

6. Why does the observed pattern of FVs occur? (Bold letters are answer choices pick best answer)  A.The future values increase because as compounding periods per year increase, interest is earned on interest less frequently. B. The future values decrease because as compounding periods per year increase, interest is earned on interest more frequently. C.The future values increase because as compounding periods per year increase, interest is earned on interest more frequently. D. The future values increase because as compounding periods per year decrease, interest is earned on interest more frequently. E.The future values decrease because as compounding periods per year decrease, interest is earned on interest more frequently.

Answer 1

Answer -

Using Formula

Future Value = P( 1 + r / n)^{n x t}

Where P = Principal

r = nominal interest rate

n = Number of compounding period

t = number of years

A)	n = 1 , t = 6	Future Value = P( 1 + r / n)n x t FV = 300 ( 1 + 0.04 / 1) 6 X 1 FV = 300 (1.04)6 FV = 300 X 1.26 FV = $378
B)	n = 2 , t = 6	Future Value = P( 1 + r / n)n x t FV = 300 ( 1 + 0.04 / 2) 6 X 2 FV = 300 (1.02)12 FV= 300 X 1.268 FV = $380.4
C)	n = 4 , t = 6	Future Value = P( 1 + r / n)n x t FV = 300 ( 1 + 0.04 / 4) 6 X 4 FV = 300 (1.01)24 FV = 300 X 1.27 FV = $381
D)	n = 12 , t = 6	Future Value = P( 1 + r / n)n x t FV = 300 ( 1 + 0.04 / 12) 6 X 12 FV = 300 (1.003)72 FV = 300 X 1.24 FV = $372
E)	n = 365 , t = 6	Future Value = P( 1 + r / n)n x t FV = 300 ( 1 + 0.04 / 365) 6 X 365 FV = 300(1.0001)2190 FV = 300 X 1.244 FV = $373.2