Question

(1 point) Hannah would like to make an investment that will turn 6000 dollars into 31000 dollars in 4 years. What quarterly rate of interest, compounded four times per year, must she receive to reach her goal? Answers percent.

Answer 1

O Hannah woud like a investment that will tur into 31000 dollars in 4 year - What quaterly rate of per year She receive to reach her goal ah woud like to make an 1 That will turn 6000 dollars nollors in 4 years mpounded apy rate of interest, Tour times per year. must We are given in this question P = 6000 - 4 year A = 31 000 Y = R LP . We use formula for compound interest compounded quarterly as - A =P ( 1 + 8 jan e. I = A-P where pa principal A = amount R = rate of interest p. a. (per anno n = number of years. we have to find. rie R using given dato A = P(1+ 31000 - 6000 (1 + r)"

16 taking log to base 10 on both sides log, (91) - log H logo Sul,6867=ıslog, (1 + i) fusing properties of hogarithm) 0172321 - 109.+ 0.044576 = log(ity Rasing both sides to power 10. . 10 = 1 + 1.108092 = 1 + 0.044576 1.108092-1 - ? 0.10892 = 2 .: r = -0.43568 R = rx100 = 0.43568 8100 = 43.560

We observe that R - 43.568 is annual ro - interest quarterly rate of interest 43.8058 = 101852 %