Question

Jimmy invests $22,000 in an account that pays 5.99% compounded quarterly. How long (in years and months) will it take for his investment to reach $25,000? years and months (Round the answer for months up to the nearest multiple of three.)

Answer 1

Given: Jimmy invests Amount Alt)= $22000 Rate of interest (R) = 5.99%. Compounded quartely. : since, we have to calculate and months) (years $ when the investment reach 25, Now, the formula for Com pound interest Alt) = A ( 1+ olnnt where Alt) in the amt at timet r is the initial investment initial investment Ao is the was number of times Compounded the per year. non of years. t is the no. 4xt 22000 = π 22ooo •[! 5.99 1oox 4 25700 14 014975 4t 220 1.13 [1.014975] 4t Taking log! both sides -

Log (1.18) - 4 tlog (1.014975) -) 0.053 ut x 6.45x103 3 - 0.053 x 10 4 X 6.45 =) 2.0542 =t 2.05 - t for month 0.05X 12 = 0.6 ~ month ta 2 years month Aus 2: Rate of investment (R)= 5% compound monthly investment double with rate 5/. compounded monthly. when the so, alt) = $44000 AoE $22000 1287 44000 11 lt 5 100x12 2*** 12t همه را با 2 2000 [ 1.00] [1.0042] 12t 2 =

on both sides - Taking Log Log (2) = 12t log (1.0042) 0.30 12tx 1.82x103 0.30 t a 13.73 12x1.828103 -- for months 0.73X12 = 8.76 ~ 9 months = (1.3 yon gmonths) become triple Aus 3: when the investment - $ 16000 Compounded continuously oate = 6% Alt) = $6600 Aor 22ood Alt) = to [ 1+2) "4 66000 22ooo It 6 It Too 3 = [1.06]t Taking on both "Log' sides log3 = log(1.06) xt o.uz - 0.025t

at 18.8 0.047 0.025 " to you a 18 years completed to become $ 66000