Question

An actor invests some money at 8​% simple​ interest, and ​$21 comma 000 more than four times the amount at 10​% simple interest. The total annual interest earned from the investment is ​$49 comma 140. How much did he invest at each​ amount? Use the​ six-step method.

Answer 1

First investment = $98000

Second = $413,000

Explanation:

Given the following :

Investment 1:

Let first investment = f

Rate = 8% = 0.08

Investment 2:

$21,000 more than 4 times of investment 1:

4f + 21000

Rate = 10% = 0.1

Total annual interest earned from both :

$49,140

Interest on investment 1 + interest on investment 2 = $49,140

To solve:

Simple Interest = principal * rate * time

Time = 1 year

Total interest = (f * 0.08 * 1) + ((4f + 21000) * 0.1 * 1)

49140 = 0.08f + 0.4f + 2100

0.48f = 47040

f = 47040 / 0.48

f = 98000 = first investment

Second investment :

4f + 21000

= 4(98000) + 21000

= $413,000