Question

$5,000 is deposited today into a bank account. The account earns 4.5% per annum compounded half yearly for the first 6 years, then 4.8% per annum compounded quarterly thereafter. Assuming no further deposits or withdrawals are made,

(a) Calculate the account balance six months from today.

(b) Calculate the account balance 6 years from today.

(c) Calculate the account balance 6.5 years from today.

(d) Calculate the account balance 10 years from today.

Answer 1

a)

Rate = 4.5% / 2 = 2.25%

Periods = 0.5 * 2 = 1

Future value in 6 months = Present value (1 + r)ⁿ

Future value in 6 months = 5,000 (1 + 0.0225)¹

Future value in 6 months = $5,112.50

b)

Rate = 4.5% / 2 = 2.25%

Periods = 6 * 2 = 12

Future value in 6 years = Present value (1 + r)ⁿ

Future value in 6 years = 5,000 (1 + 0.0225)¹²

Future value in 6 years = 5,000 * 1.30605

Future value in 6 years = $6,530.25

c)

Quarterly rate = 4.8% / 4 = 1.2%

Number of periods = 0.5 * 4 = 2

Future value in 6.5 years = 6,530.25 (1 + 0.012)²

Future value in 6.5 years = $6,687.92

d)

Number of periods = 4 * 4 = 16

Future value in 10 years = 6,530 (1 + 0.012)¹⁶

Future value in 10 years = 6,530 * 1.210287

Future value in 10 years = $7,903.17