Simple Interest
Math MCQs

Question :    Lisa took a loan of $6100 at the rate of 10% simple interest per annum. If he paid an amount of $11590 to clear the loan, then find the time period of the loan.

Correct Answer  9

Solution & Explanation

Solution

Given,

Principal (P) = $6100

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

Amount (A) = $11590

Thus, time (T) = ?

Method (1) Using Formula

Calculation of Simple Interest, when Principal and Amount are given

Formual to Calculate Simple Interest when Principal and Amount are given

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

⇒ Simple Interest (SI) = Amount – Principal

⇒ SI = $11590 – $6100 = $5490

Thus, Simple Interest = $5490

Calculation of the Time using forumula when Amount, Simple Interest and Principal are known

Formula to find the Time (T)

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

⇒ T = ^{100 × SI}/_{P × R}

Thus, Time (T) = ^{100 × 5490}/_{6100 × 10}

= ⁵⁴⁹⁰⁰⁰/₆₁₀₀₀

= 9 years (using formula)

Thus, Time (T) = 9 years (from time taken before calculation)Answer

Calculation of the Time using Unitary Method when Amount, Simple Interest and Principal are known

Here, we have

Principal (P) = $6100

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

Simple Interest = $5490 (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 $6100

= ¹⁰/₁₀₀ × 6100

= ^{10 × 6100}/₁₀₀

= ⁶¹⁰⁰⁰/₁₀₀ = 610

Thus, simple Interest for 1 year = $610

Now,

∵ If the simple Interest is $610, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₆₁₀ years

∴ If the simple Interest is $5490, then the time = ¹/₆₁₀ × 5490 years

= ^{1 × 5490}/₆₁₀ years

= ⁵⁴⁹⁰/₆₁₀ = 9 years

Thus, time (T) = 9 years Answer

Similar Questions

(1) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 4% simple interest?

(2) Patricia took a loan of $4300 at the rate of 6% simple interest per annum. If he paid an amount of $6622 to clear the loan, then find the time period of the loan.

(3) Find the amount to be paid if Christopher borrowed a sum of $6000 at 5% simple interest for 7 years.

(4) Karen took a loan of $5900 at the rate of 9% simple interest per annum. If he paid an amount of $11210 to clear the loan, then find the time period of the loan.

(5) Sarah took a loan of $5700 at the rate of 8% simple interest per annum. If he paid an amount of $10260 to clear the loan, then find the time period of the loan.

(6) What amount will be due after 2 years if Joseph borrowed a sum of $3350 at a 7% simple interest?

(7) Find the amount to be paid if Michael borrowed a sum of $5300 at 8% simple interest for 8 years.

(8) Elizabeth took a loan of $4900 at the rate of 8% simple interest per annum. If he paid an amount of $8428 to clear the loan, then find the time period of the loan.

(9) Daniel took a loan of $6200 at the rate of 10% simple interest per annum. If he paid an amount of $11780 to clear the loan, then find the time period of the loan.

(10) In how much time a principal of $3200 will amount to $3680 at a simple interest of 3% per annum?