Question

an investor has $7,500 invested at one rate and $6,200 invested at a different rate it's a second investment is at a rate 2% lower than the first find the rate for each investment if his combined annual interest income is $690

Answer 1

First investment

Amount invested = $7,500

rate = x % (unknown)

Tme = 1 year (annually)

Second investment;

Amount invested = $6,200

Rate = (x - 2)% 2% {lower than the first}

Time = 1 year

Total interest = $690

Using the simple interest formula to find the rate of each investment;

SI = PRT/100

Let Ia be the interest on first investment and Ib be that on second investement

Ia + Ib = 690

(PRT/100)a + ( PRT/100)b = 690

7500*x*1/100 + 6200(x-2)*1/100 = 690

75x + 62(x-2) = 690

75x + 62x - 124 = 690

137x = 690 + 124

137x = 814

x = 814/137

x = 5.94%

The rate in second investment = 5.94 -2 = 3.94%

Rate for first investment = 5.94%

Rate for second investment = 3.94%