Question

Helene invested a total of $1,000 in two simple-Interest bank accounts. One account paid5% annual interest; the other paid 10% annual interest. The total amount of interest sheearned after 1 year was $75. Find the amount invested in each account.In the 10% account.Helene invested sin the 5% interest account and $

Answer 1

Formula for simple interest:

A = P(1 + rt)

P = Principal

r = interest rate (r1 = 5% and r2 = 10%)

t = time in years (1 year)

In the first account:

A = P(1 + rt)

A1 = P1(1 + 0.05)

In the second account:

A2 = P2(1 + 0.10)

Also A1 + A2 = 1075

And P1 + P2 = 1000

If we use both account equations in the third equation:

A1 + A2 = 1075

P1(1 + 0.05) + P2(1 + 0.10) = 1075

1.05 P1 + 1.10 P2 = 1075

P1 = (1075 -1.10 P2)/1.05

Since P1 + P2 = 1000

then (1075 -1.10 P2)/1.05 + P2 = 1000

(1075 -1.10 P2) + 1.05 P2 = 1000 (1.05) = 1050

1075 - 1.10 P2 + 1.05 P2 = 1050

-0.05 P2 = 1050 - 1075 = -25

P2 = -25/(-0.05) = 500

P1 = 1000 - P2 = 1000 - 500 = 500

Answer:

In the 5% account Helene invested: 500

In the 10% account Helene invested: 500