Question

Matt recently deposited $27,000 in a savings account paying a guaranteed interest rate of 4 percent for the next 10 years.

A) If Matt expects his marginal tax rate to be 32.00 percent for the next 10 years, how much interest will he earn after-tax for the first year of his investment?

B) How much interest will he earn after-tax for the second year of his investment if he withdraws enough cash every year to pay the tax on the interest he earns?

C) How much will he have in the account after four years?

D) How much will he have in the account after seven years? For all requirements, do not round intermediate calculations and round your final answers to the nearest whole dollar amount.

Answer 1

Solution:

Computation of Balance in Saving Account
Period	Beginning balance	Interest earned (4% * Beginning balance)	Withdrawl for tax payment (Interest earned * 32%)	Ending balance (Beginning balance + Interest earned - Withdrawl)
0				$27,000.00
1	$27,000.00	$1,080.00	$345.60	$27,734.40
2	$27,734.40	$1,109.38	$355.00	$28,488.78
3	$28,488.78	$1,139.55	$364.66	$29,263.67
4	$29,263.67	$1,170.55	$374.57	$30,059.64
5	$30,059.64	$1,202.39	$384.76	$30,877.26
6	$30,877.26	$1,235.09	$395.23	$31,717.13
7	$31,717.13	$1,268.69	$405.98	$32,579.83
8	$32,579.83	$1,303.19	$417.02	$33,466.00
9	$33,466.00	$1,338.64	$428.36	$34,376.28
10	$34,376.28	$1,375.05	$440.02	$35,311.31

Refer above table:

Solution A:

Interest earned after tax for first year = $1,080 - $345.60 = $734

Solution B:

Interest earn after tax for second year of his investment = $1,109.38 - $355 = $754

Solution C:

Account balance after 4 years = $30,060

Solution D:

Account balance after 7 years = $32,580