Question

Burt deposits $10,000 into a bank account today. The account earns 4.5% per annum compounding daily for the first 4 years, then 3.5% 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 4 years from today.

(c) Calculate the account balance 4.5 years from today.

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

Answer 1

Solution:

Money Deposited = $10,000

Interest rate = 4.5% per annum daily compounding

Daily interest rate = 4.5%/365

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

Account Balance = 10000 * ( 1+ 4.5%/365)^180 = 10,000 * 1.02243845145584 = 10224.38

(b) Calculate the account balance 4 years from today.

Number of days in 4 years = 365* 4 = 1460

Account Balance = 10000 * ( 1+ 4.5%/365)^1460 = 10,000 * 1.197942264 = 11979.42

(c) Calculate the account balance 4.5 years from today.

After 4 year the interest rate applicable will be 3.5% per annum and compounding will be per quarter

Quarterly rate = 3.5% / 4 = 0.875%

Invested amount = 11979.42

Time period = 2 quarter

Account Balance = 11979.42* ( 1+ 0.875%)^2 = 11979.42* 1.0175765625= 12,189.98

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

Quarterly rate = 3.5% / 4 = 0.875%

Invested amount = 11979.42

Time period = 6 years = 6*4 =24 quarter

Account Balance = 11979.42* ( 1+ 0.875%)^24 = 11979.42* 1.23255170= 14,765.28