Question

Skippy has a total of $10,000 to split between two investments. One account offers 4% simple interest, and the other account offers 8% simple interest. For tax reasons, he can only earn $500 in interest the entire year. How much money should Skippy invest in each account to earn $500 in interest for the year

Answer 1

Skippy should invest $ 7500 in account offering 4 % interest and $ 2500 in account offering 8 % simple interest

Solution:

Given that Skippy has a total of $10,000 to split between two investments

One account offers 4% simple interest, and the other account offers 8% simple interest

Total interest earned = 500

Number of years = 1

Let the principal with rate of interest 4 % is x

So the principal for rate of interest 8 % is 10000 - x

Total interest earned = simple interest for 4 % interest + simple interest for 8 % interest

Simple interest is given as:

$S.I = \frac{pnr}{100}$

Where "p" is the principal and "r" is the rate of interest and "n" is the number of years

Therefore,

$\text{ Total interest earned } = \frac{x \times 1 \times 4}{100} + \frac{10000-x \times 1 \times 8}{100}$

$500 = 0.04x + (10000 - x)0.08\\\\500 = 0.04x + 800 - 0.08x\\\\-300 = -0.04x\\\\x = 7500$

Therefore skippy should invest $ 7500 in account offering 4 % interest

And skippy should invest (10000 - x) = (10000 - 7500) = $ 2500 in account offering 8 % interest