Question

A man invests 10,000 dollars in two seconds in two accounts, the first yielding 4 percent annual interest and the second, 5 percent. If x is invested in the first account, how much will the annual interest does the man earn on his investment?

Answer 1

500-0.01X

Explanation:

Total amount invested is X, account 1 pays 4% and account 2 pays 5%. Total invested is the summation of the two interests:

#First Investment at 4%:

`I=P(1+i)^1-X, P=X, i=0.04\\\\I=X(1.04)-X\\\\=0.04X`

#Interest Earned on 2nd Investment, at 5%.

`I=P(1+i)^1-X, P=(10000-X), i=0.05\\\\I=(10000-X)(1.05)-(10000-X)\\\\=10500-1.05X-10000+X\\\\=500-0.05X`

`I_(net)=I_1+I_2\\\\=0.04X+500-0.05X\\\\=500-0.01X`

Hence, the net annual investment is 500-0.01X