Question

last year Scott had $10,000 to invest. He invested some of it in an account that paid 7% simple interest per year and he invested the rest in an account that paid 8% simple interest per year. After one year he received a total of $770 in interest. How much did he invest in each account?

Answer 1

A = P(1 + rt)

Invest 1:

A1 = P1(1 + 0.07) = P1(1.07)

Invest 2:

A2 = P2(1 + 0.08) = P2(1.08)

Also P1 + P2 = 10000

And A1 + A2 = 10770 (initial principal and interests) ==> A1 = 10770 - A2

From invest 1: P1 = A1/(1.07)

From invest 2: P2 = A2/(1.08)

A1/(1.07) + A2/(1.08) = 10000

Using the value we found for A1:

(10770 - A2)/1.07 + A2/(1.08) = 10000

(10770 - A2)1.08 + A2(1.07) = 10000(1.07)(1.08) = 11556

11631.6 - 1.08A2 + 1.07A2 = 11556

- 1.08A2 + 1.07A2 = 11556 - 11631.6

-0.01A2 = -75.6

A2 = 75.6/(0.01) = 7560

A2 = 7560

Since A1 + A2 = 10770 ==> A1 = 10770 - A2 = 10770 - 7560 = 3210

A1 = 3210

P1 = A1/(1.07) = 3210/(1.07) = 3000

P1 = 3000

P2 = A2/(1.08) = 7560/1.08 = 7000

Answer:

On the first account (7% interest) Scott invested $3,000

On the second account (8% interest) Scott invested $7,000