What is the answer for question 17) ?

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Samir has $10,000 in hand which he has won in lottery. This is his principal amount. When he wants it to grow upto $1,000,000 in principal + interest @5%, he has to wait 94 years.

First we have to find the nature of the deposit scheme, i.e whether it is a simple interest scheme or a compounded one. Puttiing the formula for simple interest, the total interest to be accrued is $1,000,000-$10,000 = $990,000.

Let the time required to accrue this amount as interest be t, then

990000 = 10000*t*5/100

Or, t = 2000 years. But the problem requires it to be 94 years.

So, the rate of interest is not simple.

It must be a compounding interest scheme, if compounded annually

Then,

Amount = `P (1+R/100)^t`

Putting A = 1000000,

R = 5%

We get,

`1000000 = 10000(1+5/100)^t`

`=>` `100 = (1.05)^t`

Taking log (to the base 10) on both sides,

`=>` `Log 100 = t log 1.05`

Or, `t = log 100/ log 1.05` = 94.38 years.

Therefore, the scheme is an annually compounding one at the rate of 5% interest.

Now, let it takes n number of years to grow upto $ 500,000. putting the values in the equation for compound interest we get,

`500000 = 10000(1+5/100)^t`

Or, `50 = (1.05)^t`

Taking log (to the base 10) on both sides,

`Log 50 = t log 1.05`

Or,` t = log 50/ log 1.05 `

= 80.18 years.

**Therefore, Samir has to wait another 80 years in order to get upto a sum of $500,000.**

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