Find the amount invested at each rate. (total annual income interest given)

Question

A church building fund has invested some money in two ways: part of the money at 3% and four times as much at 2.75%. Find the amount invested at each rate if the total annual income from interest is $2800.

Answer 1

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%