mcqs Math Simple Interest Lisa took a loan of $6100 at the rate of 6% simple interest per annum. If he paid an amount of $9760 to clear the loan, then find the time period of the loan. 7915

Question: Lisa took a loan of $6100 at the rate of 6% simple interest per annum. If he paid an amount of $9760 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) = $6100

Rate of Simple Interest (R) = 6% per annum

Amount (A) = $9760

Thus, time (T) = ?

Method (1) Using Formula

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

⇒ Simple Interest (SI) = Amount – Principal

⇒ SI = $9760 – $6100 = $3660

Thus, Simple Interest = $3660

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

⇒ T = ^{100 × SI}/_{P × R}

Thus, Time (T) = ^{100 × 3660}/_{6100 × 6}

= ³⁶⁶⁰⁰⁰/₃₆₆₀₀

= 10 years (using formula)

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

Here, we have

Principal (P) = $6100

Rate of Simple Interest (R) = 6% per annum

Simple Interest = $3660 (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 = 6% of Principal

= 6% of $6100

= ⁶/₁₀₀ × 6100

= ^{6 × 6100}/₁₀₀

= ³⁶⁶⁰⁰/₁₀₀ = 366

Thus, simple Interest for 1 year = $366

Now,

∵ If the simple Interest is $366, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₃₆₆ years

∴ If the simple Interest is $3660, then the time = ¹/₃₆₆ × 3660 years

= ^{1 × 3660}/₃₆₆ years

= ³⁶⁶⁰/₃₆₆ = 10 years

Thus, time (T) = 10 years Answer