Mrs Alford invested 6100 in securities Part of the money was

Mrs. Alford invested $6100 in securities. Part of the money was invested at 7% and part at 8%. The total annual income was $443. How much was invested at each rate?

Solution

Let the amount invested at 7 % and 8 % be $ x and $ 6100 -x respectively. Then the annual income accruing to Mrs Alford is 0.07x + 0.08( 6100 -x ) . Therefore  0.07x + 0.08( 6100 -x ) = 443 or, 0.07x + 488 - 0.08x = 443 or, 0.08x - 0.07x = 488 -443 or, 0.01x = 45. Therefore, x = 4500.Thus, the amounts invested at 7 % is $ 4500 and the amount invested at 8 % is $ 6100-4500 = 1600. We can verify the result by computing annual interest @7 % on $ 4500 which is $315 and that on $ 1600 @ 8% which is $ 128. The total annula income is, therefore, $ 315 + $ 128 = $ 443. Thus, our solution is correct.