FUTURE VALUE FOR VARIOUS COMPOUNDING PERIODS Find the amount

FUTURE VALUE FOR VARIOUS COMPOUNDING PERIODS Find the amount to which $700 will grow under each of these conditions: a. 4% compounded annually for 3 years. Do not round intermediate calculations. Round your answer to the nearest cent. b. 4% compounded semiannually for 3 years. Do not round intermediate calculations. Round your answer to the nearest cent. c. 4% compounded quarterly for 3 years. Do not round intermediate calculations. Round your answer to the nearest cent. d, 4% compounded monthly for 3 years. Do not round intermediate calculations. Round your answer to the nearest cent. e, 4% compounded daily for 3 years. Do not round intermediate calculations. Round your answer to the nearest cent. f. Why does the observed pattern of FVs occur? -Select The future values increase because as compounding periods per year increase, interest is earned on interest less frequently. The future values decrease because as compounding periods per year increase, interest is earned on interest more frequently. The future values increase because as compounding periods per year increase, interest is earned on interest more frequently. The future values increase because as compounding periods per year decrease, interest is earned on interest more frequently. The future values decrease because as compounding periods per year decrease, interest is earned on interest more frequently.

Solution

a)

Future value = present value ( 1 + R)ⁿ

Future value = 700 ( 1 + 0.04)³

Future value = $787.4

b)

Number of periods = 3 * 2 = 6

Interest rate = 0.04 / 2 = 0.02

Future value = 700 ( 1 + 0.02)⁶

Future value = $788.3

c)

Number of periods = 3 * 4 = 12

Interest rate = 0.04 / 4 = 0.01

Future value = 700 ( 1 + 0.01)¹²

Future value = $788.8

d)

Number of periods = 3 * 12 = 36

Interest rate = 0.04 / 4 = 0.003333

Future value = 700 ( 1 + 0.003333)³⁶

Future value = $789.1

e)

Number of periods = 3 * 365 = 1,095

Interest rate = 0.04 / 365 = 0.00011

Future value = 700 ( 1 + 0.00011)^1,095

Future value = $789.2

f)

The future values increase because as compounding periods increase, interest is earned on interest more frequently