A sum of 1500 is invested at 5% p.a. simple interest. If the interest is added to the principal after every 10 years, the amount will become ₹ 3000 after :

$16\frac{2}{3}$ years

sum of 1500 is invested at 5% p.a. simple interest

Simple interest after (T1=10 years) = 1500*5*10/100 = 750

Amount = 2250

Since, the interest is added to the principal after every 10 years

New Principal = 2250

If Amount = 3000

Simple interest = 750

rate = 5% p.a.

T2=?

750 = 2250*5*T2/100

100 = 15*T2

T2 = 100/15 = 20/3

Total time for principal 1500 to become 3000 = 10 + 20/3 = 50/3 = 16 2/3 years

The correct answer is Option (2) → $16\frac{2}{3}$ years