Question

# Assume that you deposit \$1,000 in a bank account that promises a fixed rate of interest...

Assume that you deposit \$1,000 in a bank account that promises a fixed rate of interest of 4% per year for 10 years with annual compounding. You want to know the balance in your account at the end of 10 years. Assume that you do not make any withdrawals and that the bank stays solvent for 10 years (and thus can keep its promise to pay you in 10 years). Across the street, the savings & loan offers a similar account that is identical in all respects except that the account will have monthly compounding. Which account is the better deal, and why?

Savings & loan; insolvency rates are lower for savings & loans than banks, hence the savings & loan is more likely to be around in 10 years.

Bank; it offers a higher effective rate of interest.

Savings & loan; with monthly rather than annual compounding, interest payments have more opportunities to earn interest.

Bank; unlike a savings & loan, it can offer variable rates of interesT

Option 1:

PV = Amount deposited = \$1,000

n = 10 years

r = interest rate = 4%

Account balance in 10 years = PV * (1+r)^n

= \$1,000 * (1+4%)^10

= \$1,000 * 1.48024428492

= \$1,480.24428492

= \$1,480.24

Option 2:

PV = Amount deposited = \$1,000

n = 10*12 = 120 months

r = interest rate = 4%/12 = 0.33333333%

Account balance in 10 years = PV * (1+r)^n

= \$1,000 * (1+0.33333333%)^120

= \$1,000 * 1.49083268242

= \$1,490.83268242

= \$1,490.83

Therefore, balance in the account with monthly compounding more than annual compounding

Hence better to choose second bank with monthly compounding

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