Question

Last year, Jose had to invest. He invested some of it in an account that paid simple interest per year, and he invested the rest in an account that paid simple interest per year. After one year, he received a total of in interest. How much did he invest in each account? First account: Second account:

Answer 1

Answer:Please refer to the explanation section

Explanation:

The question is incomplete. We do not have the rate interest for both accounts. We also do not know how much is invested in each account. The question also has a typo, the question says "he invested some of it in an account that paid simple interest per year and invested the rest in an account that paid simple interest per year". We will make some assumption in order to provide a proper solution to this question

Assumptions:

Firstly we will assume he invested in a simple interest account and a compound interest account. assume

The total investment is $1000. $5000 is invested in each account.

Therefore the  Present Value (PV) is $5000 for both accounts

Interest rate (R) is 10% per year for simple interest and 10% per per year   Compounded monthly for compound interest account

Period (n) = 1 year

Simple Interest Account

Future Value (Simple Interest) = P(1 + Rn)

Future Value (Simple Interest) = $5000(1 + 0.10 x 1) = $5500

Interest from Simple interest account = 5500 - 5000 = $500

Compound interest Account

Future Value (Compound interest) = P(1 + R)^n

Future Value (Compound interest) = $5000(1 + 0.10/12)^12 = 5523.565337

Interest form Compound interest account = 5523.57 - 5000 = $523

compound interest account earned more interest than Simple interest Account

Answer 2

Answer:

Jose invests $9,000 in the first account and $1,000 in the second account.

Explanation:

let A = amount invested in first account

let B = amount invested in second account

0.08A + 0.05B = 770

A + B = 10,000

B = 10,000 - A (now replace B)

0.08A + 0.05(10,000 - A) = 770

0.08A + 500 - 0.05A = 770

0.03A = 770 - 500 = 270

A = 270 / 0.03 = 9,000

B = 10,000 - 9,000 = 1,000