Question

Changing compounding frequency???Using? annual, semiannual, and quarterly compounding ?periods, (1) calculate the future value if???$7000 is deposited initially at 9?% annual interest for 4 years and? (2) determine the effective annual rate?????(EAR?).

Annual Compounding:

Semiannual Compounding:

Quarterly Compounding:

Answer 1

1) Future value of an amount if computed as -

FV = Amount x (1 + r)ⁿ

where, r = rate of interest, n = no. of years

FV = $7000 x (1 + 0.09)⁴ = $9881.07127 or $9,881.07

2) EAR is computed as follows -

EAR = (1 + r / m)^m - 1

where, r = annual nominal rate, m = times compounded in a year

Annual compounding

m = 1

EAR = (1 + 0.09 / 1)¹ - 1 = 0.09 or 9.00%

Semi - annual compounding

m = 2

EAR = (1 + 0.09/ 2)² - 1 = 0.092025 or 9.2025% or 9.20%

Quarterly compounding

m = 4

EAR = (1 + 0.09/ 4)⁴ - 1 = 0.09308331878 or 9.308331878% or 9.31%