Roy Gross is considering an investment that pays 7.60 percent. How much will he have to invest today so that the investment will be worth $27,000 in six years? (If you solve this problem with algebra round intermediate calculations to 4 decimal places, in all cases round your final answer to the nearest penny.) Amount to be invested today $

He has to invest $16,803.32 so that the investment will be worth $27,000 in six years with a 7.6% interest rate.

Explanation:

Year 6: 27,000

Year 5: 27,000 - (27,000 x 7.6 / 100) = 27,000 - 2,052 = $24,948

Year 4: 24,948 - (24,948 x 7.6 / 100) = 24,948 - 1,896.05 = $23,051.95

Year 3: 23,051.95 - (23,051.95 x 7.6 / 100) = 23,051.95 - 1,751.95 = $21,300

Year 2: 21,300 - (21,300 x 7.6 / 100) = 21,300 - 1,618.80 = $19,681.20

Year 1: 19,681.20 - (19,681.20 x 7.6 / 100) = 19,681.20 - 1,495.77 = $18,185.42

Year 0: 18,185.42 - (18,185.42 x 7.6 / 100) = 18,185.42 - 1,382.10 = $16,803.32