Correct Answer - Option 3 : $ 60,000
Given∶
Rate of Internet = 5%
Difference between the interest of third year and first year = $ 307.50
Formula Used∶
S.I. = PRT/100
A = P(1 + R/100)n
Calculation∶
Let the sum of money be invested be $x
Rate of interest = 5% p.a.
Now,
Interest for the first year = (x × 5 × 1) / 100 = $ x/20
Interest for the 3rd year i.e. the C.I. for the third year = amount after 3 years - amount after 2 years.
C.I. for the 3rd year = x(1 + 5/100)3 - x(1 + 5/100)2
⇒ x[(21/20)3- (21/20)2]
⇒ [x × (21/20)2(21/20 - 1)]
⇒ x × 441/400 × 1/20
⇒ $ 441x/8000
Given, difference between interests of third year and first year is Rs.307.50
441x/8000 - x/20 = 307.50 = 615/2
⇒ (441 - 400)x/8000 = 615/2
⇒ 41x/8000 = 615/2
⇒ x = 615/2 × 8000/41 = $ 60,000
∴ The sum of money invested by Sunder Pichai is $60,000.