Lauren plans to deposit 3000 into a bank account at the begi

Lauren plans to deposit $3000 into a bank account at the beginning of next month and $225/month into the same account at the end of that month and at the end of each subsequent month for the next 3 years. If her bank pays interest at a rate of 6%/year compounded monthly, how much will Lauren have in her account at the end of 3 years? (Assume she makes no withdrawals during the 3-year period. Round your answer to the nearest cent.)

Solution

HEre we use the periodic payment in the future value formula. we add to that the value of $3000 drawing interest at 6% annual interest compounded monthly for 3 years.

FV = 3000(1+.06/12)^(36) + [225(1+.06/12)^(36) - 1]/(.06/12)

=3000 (1+0.005)^36 + [225 (1+0.005)^36 -1]/0.005

=3000 x 1.1967 + [225 x (1.1967 - 1)] /0.005

=3590+ (225 x 0.1967)/0.005

=3590 + 44.2575/0.005

=3590 +8851.5

=12441.5

So total last amount payable to her after 3 years is $ 12441.50.