rate principal time S interest

investment A rA $8000 4yrs SI A
investment B rB $7000 5yrs SI B

It is known that rA : rB = 2 : 3 and that investment B earned $2000 more interest than investment A. Find the values of rA, rB, SI A and SI B

2 answers

Investment A:
Rate = r.
Po = $8000.
T = 4 yrs.
Ia = Po*r*T = 8000*r*4 = 32,000r = Int. of Investment A.

Investment B:
Rate = 1.5r.
Po = $7,000.
T = 5 yrs.

Ib = Po*1.5r*T = 7000*1.5r*5 = 52,500r = Int. of investment B.

Ib = Ia+2000
52,500r = 32,000r + 2000.
20,500r = 2000
r = 0.0976 = 9.76% = Int. rate of investment A.

1.5r = 1.5 * 9.76 = 14.64% = Int. rate of investment B.
Pa = 1.0976 * 8000. = Principal after 4 yrs.

Pb = 1.1464 * 7000 = Principal after 5 yrs.
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