Question

Homework Question:

Burt deposits $10,000 into a bank account today. The account earns 4% per annum compounding daily for the first 3 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 3 years from today. (c) Calculate the account balance 3.5 years from today. (d) Calculate the account balance 10 years from today.

Answer 1

Deposit = $ 10,000

Assuming 30 days a month

Interest Rate (i)

Upto 3 Years = 4% p.a Compounding Daily

Thereafter = 3.5 % p.a. Compounded Quarterly

(a) Account Balance 6 months from today.

Amount = P * (1+i)^n

Amount = $ 10,000 * (1+ (0.04/365))^(6*30)

Amount = $ 10,000 * 1.0199

Amount = $ 10,199.21

(b) Account Balance from 3.5 Years from Today

Interest Rate (i)

Upto 3 Years    = 4% p.a Compounding Daily

Next 0.5 Years = 3.5 % p.a. Compounded Quarterly

Account Balance 3 years from today.

Amount = P * (1+i)^n

Amount = $ 10,000 * (1+ (0.04/365))^(3*12*30)

Amount = $ 10,000 * 1.1256

Amount = $ 11,256 (approx)

Account Balance 3.5 years from today.

Amount = $ 11,256.38 * (1+ (0.035/4))^(2)

Amount = $ 11,256.38 * 1.0176

Amount = $ 11,454 (approx)

(c) Account Balance from 10 Years from Today

Interest Rate (i)

Upto 3 Years    = 4% p.a Compounding Daily

Next 7 Years = 3.5 % p.a. Compounded Quarterly

Account Balance 10 years from today.

Amount = $ 11,256.38 * (1+ (0.035/4))^(7*4)

Amount = $ 11,256.38 * 1.27621

Amount = $ 14,366 (approx)