Question

What annual rate of interest compounded quarterly should one obtain if it is desired that one's investment becomes 3 times in 10 and half years ?​

Answer 1

Answer:

compound rate of interest expressed as a percentage shows the cumulative amount that an invested sum of money will increase per annum.

Hence, 1010 percent tells us that, after every 11 year, the amount of money in the account will increase by 110110 th (or 1.11.1 times) of the present amount.

Take the amount in the account now to be XX and the amount required to be 3X3X. We know that the value of a principal (initial) investment PP with interest rate RR after some time (years) tt will become some new amount AA, as demonstrated by the following relationship:

A=P(1+R)tA=P(1+R)t

This formula makes more sense when you realise that it is just multiplying the initial amount continuosly by 1.11.1 the amount of years it has been kept invested. Hence:

3X=X(1+0.1)t3X=X(1+0.1)t

3=1.1t3=1.1t

T=log1.13T=log1.1⁡3

Thus, finally:

t=11.53t=11.53

Therefore, 11.5311.53 years.

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