Question

A man has Php 45,000 which he invests partly at a simple interest of 5% and the rest at 3 1/2 % per annum. The annual income from 3 1/2 % investment exceeds the income from the 5% investment by Php 65. Represent the amount of each investment.

Answer 1

Answer:

Let x be the amount he invests in 5%

Then the amount he invests in 3 1/2 % is 45000-x

(45000-x)(7/2)/100 -x(5)/100=65

(45000-x)×7-10x=65×200

315000-7x-10x=13000

17x=(315-13)×1000

x=302000/17

Other amount is ,45000-302000/17

Answer 2

The value of amount of 5% investment is Php 22306.95  and for  3 1/2 % investment Php. 22693.05.

Step-by-step explanation:

Given:

A man has Php 45,000. Invests partly at a simple interest of 5% and the rest at 3 1/2 % per annum.

The annual income from 3 1/2 % investment exceeds the income from the 5% investment by Php 65.

To Find:

The value of amount of 5% investment and 3 1/2 %.

Formula Used:

$SI=\frac{QRS}{100}$      -------- formula no.01.

Where:

SI = simple interest

Q = principal

R = interest rate (in percentage)

S= time duration (in years)

Amount (A) = Principal (Invested amount)+ Simple Interest (SI)  -- formula no.02.

Solution:

As given-a man has Php 45,000. Invests partly at a simple interest of 5% and the rest at 3 1/2 % per annum.

Let man investment    Php k  at a simple interest of 5%.

So,the investment Php ( 45000-k) will be for 3 1/2 % per annum.

Considering a simple interest of 5% investment.

Applying formula no.02.

Annual Income $=Q+\frac{Q\times5\times1}{100}$

                         $=Q+0.05Q =1.05Q$

As given-The annual income from 3 1/2 % investment exceeds the income from the 5% investment by Php 65.

Considering a simple interest of 3.5% investment.

Applying formula no.02.

Annual Income$=(45000-Q)+\frac{(45000-Q)\times3.5\times1}{100}$

                        $=(45000-Q)+0.035(45000-Q)$

                       $=1.035( 45000-Q)$

As given -the annual income from 3 1/2 % investment exceeds the income from the 5% investment by Php 65.

$1.035(45000-Q)= 1.05Q+65$

$1.035\times45000-1.035Q=1.05Q+65$

$46575-1.035Q=1.05Q+65$

$46575-65=1.05Q+1.035Q$

$46510=2.085Q$

$Q=22306.95 Php$

The value of amount of 5 %  investment  = Q $= 22306.95 Php$

The value of amount of 3 1/2 %  investment =45000-Q

                                                                        $=45000 - 22306.95$

                                                                        $= 22693.05 Php$

Thus,the value of amount of 5% investment is Php 22306.95  and for  3 1/2 % investment Php. 22693.05.

PROJECT CODE#SPJ3