A man deposited one-fourth of his capital at 16% annual interests, one-third at 15% annual interests. The remaining capital should be invested at what rate of annual interests so that he can receive an average 19% interests per year?

A man deposited one-fourth of his capital at 16% annual interests, one-third at 15% annual interests. The remaining capital should be invested at what rate of annual interests so that he can receive an average 19% interests per year? Correct Answer 24%

Given:

A man deposited one-fourth of his capital at 16% annual interest.

He deposited one-third at 15% annual interests.

Average interest per year = 19%

Formula used:

S.I = (P × r × t)/100  

where P = Sum of money, r = Rate, and t = Time

Calculation:

Lets consider rate be r%

Remaining capital = 1 – (1/4 + 1/3) = 1 – 7/12 = 5/12

So Average rate of interests,

(16 × 1/4) + (15 × 1/3) + (r × 5/12)

= 4 + 5 + 5r/12

= 9 + 5r/12

According to the question,

9 + 5r/12 = 19

⇒ 5r/12 = 10

⇒ r = 10 × (12/5)

⇒ r = 24

∴ The remaining capital should be invested at 24% rate of annual interests.