1) $R / $S = total return in decimal form, let's call this TR
2) [x(a)] + (1 - x)(b) = TR, and reduce...
xa + b - xb = TR
xa - xb = TR - b
it's a little easier to show you the rest with an example...
example: $1000 total, interest earned is $32, a = 0.02, b = 0.05
32 / 1000 = 0.032 TR
x(0.02) + (1 - x)(0.05) = 0.032
0.02x + 0.05 - 0.05x = 0.032
-0.03x = -0.018
x = -0.018 / -0.03
x = 0.60, or 60% of the total $ was invested at 2%, thus (1 - x) = 0.40, or 40% was invested at 5%
x($1000) = 0.60 * 1,000 = $600 and
(1 - x)($1,000) = 0.40 * 1,000 = $400
check math:
$600 * 0.02 = $12
$400 * 0.05 = $20
total interest: $32
2) equally weighted: 1/3 = 0.3333, again, using decimal forms of rates, here "x" equals total $
0.3333x(a1%) + 0.3333x(a2%) + 0.3333x(a3%) = $S
The first one:
A guy received $ S as royalty for his book. he invested part of it in bonds paying a % interest annually. The rest he invested in a life insurance policy paying b % interest annually. If the total interest from the investments after 1 year is $R, how much did he invest in bonds? (Enter S, a, b and R, calculate investments and output result)
2. When equal amounts are invested in each of three accounts paying a1% a2% and a3% interest, one year's combined interest income is $S. How much is invested in each account?(Input a1, a2, a3and S. Calculate and output result)
