[Coogs]

If you just average your 4 percentages, you are close to begin with at 6.4%.

So let's say you invest $4000.

25%, or $1000, at each of the 4 rates....

1000 at 8.5% = 85.00
1000 at 9.2% = 92.00
1000 at 3.1% = 31.00
1000 at 4.8% = 48.00

for a total of 256.00.

256.00/4000 = .064 = 6.4%

260.00/4000 = .065 = 6.5%

So therefore you need to find a way to get $4.00 more back on you investment.

I'm going to use the 9.2% and the 4.8% and the 1000.00 at each rate

We made 140 dollars at those two rates combined. We need 144 dollars to get to 260 dollars.

X = amount invested at 9.2%
2000 - X = amount invested at 4.8%

.092X + .048(2000 - X) = 144.00
.092X + 96.00 - .048X = 144.00
.044X = 144.00 - 96.00
.044X = 48.00
X = 48.00/.044
X = 1090.91


2000 - 1090.91 = 909.09

What percent of 1000 is 1090.91?

109.1%

109.1% of your original investment, which was 25%, is

25 times 1.091 = 27.275

What percent of 1000 is 909.09?

90.9%

90.9% of you original investment, which was 25%, is

25 times .909 = 22.725

So, your your percentages to be invested at each rate to give you a 6.5% return...

25% of your money at 8.5%
25% of your money at 3.1%
27.275% of your money at 9.2%
22.725% of your money at 4.8%

This is just one solution, but it will work for any amount that you choose to invest.