Rodrigo S. answered • 08/14/19

Harvard Alum Industry Leader - Econ & Tech

Short answer:

2800 = (1/5*x*0.03) + (4/5*x*0.0275)

x=100,000 => 1/5x=20,000 =>4/5x=80,000

Step-by-step:

To answer this problem, first find the proportions/ratio of each investment, find the relative interest for each proportion, and finally find the total investment. Once you have the total investment, simply multiply by each proportion.

**a) Find the proportions. For the second part to be four times as much the first, there must be five parts in total. **

Total principal amount = x

Part 1 principal amount = 1/5x

Part 2 principal amount = 4/5x

(orange area is four times the grey area, and orange area is 4/5 of the total, while grey area is 1/5 of the total)

Or, in mathematical form b=4a, a+b=1 => a=1/5, b= 4/5

**b) Find the interest. Interest is simply the principal times the rate**

Part 1 interest = 1/5x*3%

Part 2 interest = 4/5x*2.75%

**c) Find the total investment. Total Interest is the sum of each part interest**

Total interest = (Part 1 interest) + (Part 2 interest)

Total interest = 2800

2800 = (1/5x*3%) + (4/5x*2.75%)

x = 100,000

**d) Find the investment for each part. The amount invested at each rate is principal times the portion invested**

Part 1 principal amount = 1/5*x = 1/5*100,000 = 20,000

Part 2 principal amount = 4/5*x = 4/5*100,000 = 80,000

**Answer**: 20,000 at 3% and 80,000 at 2.75%