maths問題(15)

Q.202
Initial=$75000
interest=12% p.a.=1% p.m.
payment=5000
After first month, he owes
(75000*1.01-5000)=70750
After second month, he owes 66457.5
After third month, he owes 62122.075=$62122

Q.203
After three months, the capital became
80000*1.005^3=81206.01
half of this amount remains in the old account=40603.005
Value three months later
=40603.005^1.005^3
=41215.100
The other half is invested at 9% p.a. compounded monthly
=40603.05*1.0075^3
=41523.44

Total value of investment
=41215.1+41523.44
=82738.54
=$82738

Q.204
Principal=10000
interests=7% and 6%
Final value of investment
=$10670
a)
Amount invested in plan A (7%)
=(670-600)/(700-600)*10000
=$7000
b)
Amount invested in plan B(6%)
=(700-670)/(700-600)*10000
=$3000

Q.205
a.
Proceeds=100000*1.005^(5*12)=134885.015
b.
proceeds=(100000*1.0125^8)*(1.02^12)=$140075.54
c.
It is more profitable to invest in plan 2.