Question

1. Bank A offers a savings account with interest rate of 2% compounded quarterly. Bank B offers a savings account with interest rate of 2.25% compounded semi-annually. Assume customer can deposit $5,000 and leave it on deposit for 4 years. What would be the final value for each bank account?

Answer 1

Compounding interest means that interest calculated on principal as well as on interest that has already been earned.

If compounded quarterly then time gets multiplied by 4 and rate divided by 4.

If compounded semi-annually then time gets doubled and rate divided by 2.

To calculate final value, formula is

Final Value = Present value*(1 + r)ⁿ

where,

r = Rate of interest

n = Number of years

For Bank A :

Final Value = $5000*[1 + (0.02/4)]^4*4

Final Value = $5000*(1 + 0.005)¹⁶

Final Value = $5000*(1.005)¹⁶

Final Value = $5000*1.08307

Final Value = $5401.85 or $5402

For Bank B :

Final Value = $5000*[1 + (0.0225/2)]^4*2

Final Value = $5000*(1 + 0.01125)⁸

Final Value = $5000*(1.01125)⁸

Final Value = $5000*1.09362

Final Value = $5468.10 or $5468

Hence, Bank value B ($5468) is more than Bank value A ($5402) so customer should invest in Bank B to earn more interest.