Thomas wants to save money for a vacation. Thomas invests $1,500 in an account that pays an interest rate of 6.75%. How many years will it take for the account to reach $7,300? Round your answer to the nearest hundredth

Question

anonymous · Answer

5800 = 1500 x 6.75 x t / 100

amistre64 · Answer

1500(1.0675)^t=7300

amistre64 · Answer

t = log(73/15)
     ----------
      log(1.0675)

amistre64 · Answer

log(73 / 15) / log(1.0675) = 24.2256916

amistre64 · Answer

24.22  or maybe .23

anonymous · Answer

can you show me how you get that?

amistre64 · Answer

sure..... me or him?  lol

anonymous · Answer

bt i used simple interest

anonymous · Answer

u used compound interest amistre

anonymous · Answer

amistre

amistre64 · Answer

i did :)

amistre64 · Answer

the principle investment is 1500; and you mulitply that by( 1+.0675)^t

anonymous · Answer

but which approach is correct?

amistre64 · Answer

1500(1.0675)^t = 7300 ; /1500 both sides

(1.0675)^t = 7300/1500 = 73/15

amistre64 · Answer

take the log of base (1.0675) to each side to get:

log1.0675(1.0675^t) = log1.0675(73/15)  / factor the ^t

t log1.0675(1.0675) = log1.0675(73/15)

logB(B) = 1 so.......

t = log1.0675(73/15)

amistre64 · Answer

change of base allows us to modify the right side to something we can use on a calculator

amistre64 · Answer

logB(x) = log(x)/log(B)

amistre64 · Answer

t = log(73/15)/log(1.0675)

anonymous · Answer

thank you for clearing it up for me!

amistre64 · Answer

:)  no prob, i figure in 3 days ill forget it anyways so its good to write it down lol

anonymous · Answer

lol yeah that's true. i just posted another question also. just need to know if i got the right answer & used the right equation for once!