Question

Time value Personal Finance Problem You have $3.300 to r vest today at 7% nterest compounded annualy a. Find how much you will have accumulated in the account at the end of (1) 6 years, (2) 12 years, and (3) 18 years b. Use your tindings in part a to calculate the amount of interest earned in (1) the trst 6 years ovears 1 to 6), (2) the second 6 years Gears 7 to 12and the hrd 6 years (Gears 13 1o 18) c. Compare and contrast your findings in part b. Explain a. (1) Al the end (2) At the end of 12 years, the amount you will have accumulated is s(Round to the nearest cent) (3) At the end of 18 years, the amount you wil have accumulated is Round to the nearest cent) b. (1) From your findings in part a, the amount of interest earned in the frst 6 years (years 1 to 6) is s (Round to the nearest cent) (2) From your findings in part a the amount of interest earned in the second 6 years (years 7 to 12) Is (Round to the nearest cent) (3) From your findings in part a the amount of interest earned in the third 6 years (years 13 to 18) sRound to the nearest cent) c. According to the findings in part b, the amount of interest earned how the amount of interest eamed changes in each succeeding 6-year peniod of 6 years, the amount you will have accumulated iRound to the nearest cent) n each succeeding 6-year period due to compounding (Select from the drop-down menu.)

Answer 1

Investment made=$3,300

Interest rate=7% compounded annually

$Amount=Principal(1+rate)^{years}$

a) For 6 years, amount accumulated=3,300(1+0.07)⁶=3,300*1.501=$4,953

  For 12 years, amount accumulated=3,300(1+0.07)¹²=3,300*2.2522=$7,432

For 18 years, amount accumulated=3,300(1+0.07)¹⁸=3,300*3.3799=$11,154

b) Interest earned in first 6 years=$(4,953-3,300)=$1,653

  Interest earned in second 6 years(7-12)=$(7,432-4,953)=$2,479

  Interest earned in third 6 years(7-12)=$(11,154-7,432)=$3,722

c) We can see that between years 13-18, the amount of interest earned is the highest. This teams longer the time period more interest will be earned.

Thus according to the findings in part b, the amount of interest earned increases in each 6-year period due to compounding.