Question

Jack has a saving account of value $65,550 at the start. The saving account has an interest rate of 3% that is compounded every six months. How long will it take Jack to have $100,000 in his account?

Answer 1

Given:

Principal value = $65,550

Rate of interest = 3% compounded every six month

To find:

The taken to have $100,000 in Jack's account.

Solution:

The formula for amount is

$A=P(1+\dfrac{r}{n})^{nt}$

where, P is principal, r is rate of interest, n is number of times interest compounded in an year, t is time in number of years.

Interest compounded every six month. It means, interest compounded 2 times in an year.

Substitute A=100000, r=0.03 and n=2 in the above formula.

$100000=65550(1+\dfrac{0.03}{2})^{2t}$

$\dfrac{100000}{65550}=(1+0.015)^{2t}$

$1.525553=(1.015)^{2t}$

Taking log on both sides.

$\log (1.525553)=\log (1.015)^{2t}$

$\log (1.525553)=2t\log (1.015)$

$\dfrac{\log (1.525553)}{2\log (1.015)}=t$

$t=14.1838928$

$t\approx 14.18$

Therefore, after 14.18 year the amount will reach at $100,000 or we can say that in 15th year the amount will reach at $100,000.