Question

Burt deposits $10,000 into a bank account today. The account earns 4% per annum compounding daily for the first 2 years, then 4.5% per annum compounded quarterly thereafter. No further deposits or withdrawals will be made.

For this question, assume all months are of equal length and ignore leap years.

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

(b) Calculate the account balance 2 years from today.

(c) Calculate the account balance 2.5 years from today.

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

Answer 1

Amount deposited today = 10000

The account earns 4% per annum compounding daily for the first 2 years

all months are of equal length, so number of days in a year = 30*12 = 360

So daily return for the first 2 years = 4%/360 =0.011%

(a) the account balance six months (180 days ) from today. = 10000( 1 + 0.00011)^180

= 10202 $

b) the account balance 2 years(720 days ) from today. = 10000( 1 + 0.00011)^720

=10832.82 $

The interest rate after 2 years , 4.5% per annum compounded quarterly

So interest per quarter = 4.5/4 = 1.125%

c)the account balance 2.5 years from today.

= Interest after 2 years @4% and then compounded for (0.5*4=) 2 quarters

= 10832.82( 1+ 0.01125)^2

= 11077.93 $

d)

the account balance 10 years from today.

=Interest after 2 years @4% and then compounded for (8*4 = ) 32 quarters,

=10832.82( 1+ 0.01125)^32

=15495.83 $