mcqs Math Simple Interest Betty took a loan of $6500 at the rate of 10% simple interest per annum. If he paid an amount of $13000 to clear the loan, then find the time period of the loan. 8043

Question: Betty took a loan of $6500 at the rate of 10% simple interest per annum. If he paid an amount of $13000 to clear the loan, then find the time period of the loan.

(A)  7.5
(B)  12.5
(C)  10
(D)  15

Correct Answer 10

Solution And Explanation

Solution

Given,

Principal (P) = $6500

Rate of Simple Interest (R) = 10% per annum

Amount (A) = $13000

Thus, time (T) = ?

Method (1) Using Formula

We know that, Amount (A) = Principal (P) + Simple Interest (SI)

⇒ Simple Interest (SI) = Amount – Principal

⇒ SI = $13000 – $6500 = $6500

Thus, Simple Interest = $6500

Time (T) = ^{100 × Simple Interest}/_{Principal × Rate of Interest}

⇒ T = ^{100 × SI}/_{P × R}

Thus, Time (T) = ^{100 × 6500}/_{6500 × 10}

= ⁶⁵⁰⁰⁰⁰/₆₅₀₀₀

= 10 years (using formula)

Thus, Time (T) = 10 years (from time taken before calculation)Answer

Here, we have

Principal (P) = $6500

Rate of Simple Interest (R) = 10% per annum

Simple Interest = $6500 (As calculated above by subtracting Principal from the Amount given)

We know that, interest is calculated on the basis of the Principal.

This means Simple Interest for 1 year = Rate of simple interest × Principal

Thus, Simple Interest for 1 year = 10% of Principal

= 10% of $6500

= ¹⁰/₁₀₀ × 6500

= ^{10 × 6500}/₁₀₀

= ⁶⁵⁰⁰⁰/₁₀₀ = 650

Thus, simple Interest for 1 year = $650

Now,

∵ If the simple Interest is $650, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₆₅₀ years

∴ If the simple Interest is $6500, then the time = ¹/₆₅₀ × 6500 years

= ^{1 × 6500}/₆₅₀ years

= ⁶⁵⁰⁰/₆₅₀ = 10 years

Thus, time (T) = 10 years Answer