10點!! f.3 maths~ Simple and compound interest

1)Alice deposits $1000 in a bank for 6 years on simple interest. The interest rate for the first 2 years is 1% p.a, for the following 2 years is 2% p.a. and 3% p.a, for the remaining period. Find the amount after 6 years.

1000*(1+1%)^2*(1+2%)^2*(1+3%)^(6-2-2)
=1000*(1.01)^2*(1.02)^2*(1.03)^2
=$1124.95(2 sig.fig)

2)$10000 is deposited for 1 year at an interest rate of 12% p.a. Find the difference in amount if the interest is compounded half-yearly and compounded quarterly.

Interest compounded quarterly - Interest compounded half-yearly
={10000*[1+12%/4]^4-10000} - {10000*[(1+12%/2)]^2-10000}
= 1255.1-1236
= $19.1(1 sig.dig)

1)$1000*(1+1%*2)*(1+2%*2)*[1+3%*(6-2-2)]
=$1000*(1+0.01*2)*(1+0.02*2)*(1+0.03*2)
=$1000*(1+0.02)*(1+0.04)*(1+0.06)
=$1000*(1.02)*(1.04)*(1.06)
=$1020*1.04*1.06
=$1060.8*1.06
=$1124.448
=$1124.4(corr.to 1 d.p.)

2)the amount is if the interest is compounded half-yearly
=$10000(1+12%/2)^2
=$10000(1+6%)^2
=$10000(1.06)^2
=$11236

the amount is if the interest is compounded quarterly
=$10000(1+12%/4)^4
=$10000(1+3%)^4
=$10000(1.03)^4
=$11255.0881
=$11255(corr. to nearest $1)

the diffenrent is
=$(11255-11236)
=$19