Question

a man deposits a fixed amount of money in the beginning of every month in a bank which gives 10% simple interest per year , if the total interest in the end of a year is 117 , calculate the monthly deposit

Answer 1

@hossam do you have the answer?

Answer 2

yes its 180

Answer 3

Okay, I thought something else let me try again

Answer 4

okay !!!!!

Answer 5

Bank will give interest for deposit depending on time, His each deposit will earn a different interest.
His first deposit will earn interest for 12 months or 12/12 years
His second deposit will earn interest for 11 months or 11/12 years
His third deposit will earn interest for 10 months
similarly
His twelfth deposit will earn interest for 1 month or 1/12 years
Let his each deposit be P
so first deposit will earn interest i1
\[i1=P \times R \% \times t\]
or
\[i1= \frac{P \times R \times 12}{100 \times 12}\]
R=10 so we get
\[i1=\frac{P \times 12}{10 \times 12}\]
for second deposit
\[i2=\frac{P \times 11}{10 \times 12}\]
for third deposit
\[i2=\frac{P \times 10}{10 \times 12}\]
similarly we can write for each month
for last deposit
\[i12=\frac{P \times 1}{10 \times 12}\]
so total interest
\[i=i1+i2+i3+....+i12\]
we are given the total interest is 117
so
\[117=\frac{P \times 12}{10 \times 12}+\frac{P \times 11}{10 \times 12}+........+\frac{P \times 1}{10 \times 12}\]
I have written only few terms above, let's take common term out on right hand side
\[117=\frac{P}{10 \times 12}(12+11+10+9+8+7+6+5+4+3+2+1)\]
we get now
\[117=\frac{P}{10 \times 12}(78)\]
\[P= \frac{117 \times 10 \times 12}{78}\]
so we get
\[P=1.5 \times 10 \times 12= 180\]
so his each deposit is 180

Answer 6

Did you understand?

Answer 7

thanks a million , yes i did