Question

A woman makes a deposit of 1600 shillings in an account which pays a compound interest at a rate of 6%per annum.how much was the investment after 12 years.after how many years will the investment be 3 times its value?

Answer 1

Answer:

The investment after 12 years is 3219.514 shillings.

After 19 years the investment will be 3 times its value.

Step-by-step explanation:

Given:

Principal, P = 1600 shillings

Rate of interest, R = 6% p.a.

No. of years, n = 12 years

We need to calculate the amount “A” after 12 years of investment.

Therefore,  

A = P (1 + R/100) ⁿ

   = 1600 * (1 + 6/100) ^ 12

   = 1600 * (53/50) ^ 12

   = 3219.514 shillings

Now, we also have been asked to calculate the no. of years when the investment becomes 3 times its value.

So, we can deduce from the given information that A = 3 * P.

Therefore,

A = P (1 + R/100) ⁿ

Or, 3 P = P (1+ 6/100) ⁿ

Or, 3 = (53/50) ⁿ ……………… (dividing P on both sides)

Or, 3 = (1.06) ⁿ

Or, ㏒ 3 = ㏒ (1.06) ^ n …………….(taking ㏒ on both the sides)

Or, ㏒ 3 = n ㏒ (1.06) ………………( since ㏒ x ⁿ = n log x)

Or, n = ㏒ 3 / ㏒ (1.06)

Or, n = 0.47712 / 0.02530

Or, n = 18.85 ≈ 19 years

......... (rounding off to the nearest values as year cannot be taken in decimal)