Question

After graduating college, you receive $10,000 and decide to put it in a high yield saving account. The account earns 0.50% compounded quarterly. a) (8 points) What is the effective annual interest rate? b) (7 points) If you leave your initial investment of $10,000 in the account without any withdrawals what would you expect the value of the account to be after 4 years?

Answer 1

a)

The effective annual interest rate is 0.5009%

b)

I will expect $10,201.88 the value of the account after 4 years

Step-by-step explanation:

a)

Use the following formula to calculate the effective annual interest rate

Effective annual Interest rate = ( ( 1 + Interest rate / Compounding period per year )^Compounding period per year ) - 1

Where

Interest rate = 0.50%

Compounding period per year = 4 quarters in a year

Placing values in the formula

Effective annual Interest rate = ( ( 1 + 0.5% / 4 )^4 ) - 1 = 0.005009 = 0.5009%

b)

Use the following formula to calculate the value after 4 years

Value after 4 years = Current Investment x ( 1 + Periodic Interest rate )^numbers of period

Where

Current Investment = $10,000

Periodic Interest rate = 0.50% / 4 = 0.125%

Numbers of period = Compounding Periods per year x Numbers of years = 4 quarters per year x 4 years = 16 quarters

Placing values in the formula

Value after 4 years = $10,000 x ( 1 + 0.125% )^16

Value after 4 years = $10,201.88