Question

A man decided to invest at his local bank, in a $10,000 5-year deposit certificate that pays an interest rate of 3.5% annually (single interest). Suppose the interest payment is sent annually in a check to his home and that this money is taxable. When the certificate matures, he will receive his $10,000 return (non-taxable amount). The marginal tax rate for this man is 24% and overall inflation is expected to be 2% per year.

Determine for this investment instrument:

(a) The rate of return before taxes, ignoring inflation.

(b) The rate of after-tax return, ignoring inflation

(c) The rate of return after tax, considering inflation.

Answer 1

Solution:

Initial deposit =$10,000

Interest rate = 3.5%

Annual interest = 3.5% * 10,000 = $350

After tax annual interest = $350 * (1-tax) = 350 * (1-0.24) = $266

Part A ) The rate of return before taxes, ignoring inflation

Total amount received = 350 *5 +10,000 =

Rate of return = ( Final amount / initial amount )^(1/year)= (11750 /10000)^(1/5) - 1 = (1.175)^0.2 -1 = 3.28%

Part B ) The rate of after-tax return, ignoring inflation

Total amount received = 266*5 +10,000 = 11330

Rate of return = ( Final amount / initial amount )^(1/year)= (11330 /10000)^(1/5) - 1 = (1.133)^0.2 -1 = 2.53%

Part C ) The rate of return after tax, considering inflation.

The return calculated in part B is the nominal rate of return

The real rate of return = Nominal rate of return - inflation = 2.53% - 2% = 0.53%