Question

as part of your retirement package, your company has agreed to pay you monthly payments over the next three years that have the following characteristics.

1. you will receive 12 monthly payments each year, with the first payment for the year being made on January 1st, and the last payment for the year being made on December 1st
2. monthly payments for the first year will be $4,000 per month.
3. after year 1, you will receive an annual cost of living adjustment (COLA) of 10 percent that will be effective as of the January 1st payment for each subsequent year. That is, in Year 2, your monthly payment will be 1.0 percent higher than in Year 1 (i.e. $4,000*1.01=$4.040), and in Year 3, it will be 1.0 percent higher than in Year 2.
4. you believe that interest rates will increase in the future and that you will be able to deposit your payments into an investment account and receive the following effective annual rates of return (over the 12 months fro January 1st to December 31st of each year): Years 1 and 2 = 6.6759627%, Year 3(and after)= 8.2139158%

Given this information, determine how much you should expect to have in your investment account one month after your 36th deposit, on December 31st of Year 3.

Answer is whole dollars, rounded to the nearest dollar, with no punctuation. For example, if your answer is $150,224.75, enter “150225

Answer 1

Answer:

Effective annual rates of return (over the 12 months fro January 1st to December 31st of each year): Years 1 and 2 = 6.6759627%

Monthly Interest rate = (1 + 6.6759627%) ^1/12 - 1 = 0.0054

Effective annual rates of return (over the 12 months fro January 1st to December 31st of each year): Year 3(and after)= 8.2139158%

Monthly Interest rate = (1 + 8.2139158%) ^1/12 - 1 = 0.0066

Year 1:

Monthly payments for the first year will be $4,000 per month paid on start of each month

Amount at end of year 1:

FV (rate, nper, pmt, pv, type)

= FV (0.0054, 12, -4000, 0, 1)

=49718.613796

Year 2:

Monthly deposit in year 2 = 4000 *(1 + 1%) = $4,040

Amount at end of year 2:

= FV (0.0054, 12, -4040, -49718.613796, 1)

=103253.6098

Year 3:

Monthly deposit in year 3 = 4040 *(1 + 1%) = $4,080.4

Amount at end of year 3:

= FV (0.0066, 12, -4080.40, -103253.6098, 1)

=162851.84

=162852

Amount you should expect to have in your investment account on December 31st of Year 3 = 162852