Question

Changing compounding frequency Using​ annual, semiannual, and quarterly compounding​ periods, (1) calculate the future value if ​$5 comma 000 is deposited initially at 12​% annual interest for 5 ​years, and​ (2) determine the effective annual rate ​(EAR​).

Answer 1

a). Future value=$8,811.71

effective annual rate is=12%

B. Future value =$8,954.23

effective annual rate=12.36%

C Future value quarterly=$9,030.56

effective annual rate=12.55%

Step-by-step explanation:

The formula to be used =

FV = PV (1 + r/m)^mn

FV = Future value

PV = Present value = $5,000

R = interest rate = 12​%

M = number of compounding per year

N = number of years = 5

Formula for effective annual rate = (1 + r/m) ^m - 1

1. Annual compounding

$5,000 x (1 + 0.12)^5 = $8811.71

EAR = (1.12)^1- 1 = 0.12= 12%

2. semiannual

$5,000 x (1 + 0.12 /2)^10 = $8954.24

EAR =(1 + 0.12 / 2 )^2- 1 = 0.1236 = 12.36%

quarterly

$5,000 x (1 + 0.12 /4) ^ 20=$9,030.56

EAR = (1 + 0.12 / 4 )^4 - 1 = 12.55%

I hope my answer helps you