Simple Interest
Math MCQs

Question :    Lisa took a loan of $6100 at the rate of 8% simple interest per annum. If he paid an amount of $10492 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) = 8% per annum

Amount (A) = $10492

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 = $10492 – $6100 = $4392

Thus, Simple Interest = $4392

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 × 4392}/_{6100 × 8}

= ⁴³⁹²⁰⁰/₄₈₈₀₀

= 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) = 8% per annum

Simple Interest = $4392 (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 = 8% of Principal

= 8% of $6100

= ⁸/₁₀₀ × 6100

= ^{8 × 6100}/₁₀₀

= ⁴⁸⁸⁰⁰/₁₀₀ = 488

Thus, simple Interest for 1 year = $488

Now,

∵ If the simple Interest is $488, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₈₈ years

∴ If the simple Interest is $4392, then the time = ¹/₄₈₈ × 4392 years

= ^{1 × 4392}/₄₈₈ years

= ⁴³⁹²/₄₈₈ = 9 years

Thus, time (T) = 9 years Answer

Similar Questions

(1) Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 2% simple interest.

(2) William took a loan of $5000 at the rate of 8% simple interest per annum. If he paid an amount of $8200 to clear the loan, then find the time period of the loan.

(3) In how much time a principal of $3000 will amount to $3120 at a simple interest of 2% per annum?

(4) James took a loan of $4000 at the rate of 8% simple interest per annum. If he paid an amount of $6880 to clear the loan, then find the time period of the loan.

(5) If Richard borrowed $3600 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.

(6) Nancy took a loan of $6300 at the rate of 8% simple interest per annum. If he paid an amount of $10332 to clear the loan, then find the time period of the loan.

(7) Charles took a loan of $5800 at the rate of 6% simple interest per annum. If he paid an amount of $8584 to clear the loan, then find the time period of the loan.

(8) Calculate the amount due if Christopher borrowed a sum of $4000 at 6% simple interest for 4 years.

(9) Find the amount to be paid if Susan borrowed a sum of $5650 at 5% simple interest for 7 years.

(10) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 10% simple interest?