Simple Interest
Math MCQs

Question :    Daniel took a loan of $6200 at the rate of 9% simple interest per annum. If he paid an amount of $9548 to clear the loan, then find the time period of the loan.

Correct Answer  6

Solution & Explanation

Solution

Given,

Principal (P) = $6200

Rate of Simple Interest (R) = 9% per annum

Amount (A) = $9548

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 = $9548 – $6200 = $3348

Thus, Simple Interest = $3348

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 × 3348}/_{6200 × 9}

= ³³⁴⁸⁰⁰/₅₅₈₀₀

= 6 years (using formula)

Thus, Time (T) = 6 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) = $6200

Rate of Simple Interest (R) = 9% per annum

Simple Interest = $3348 (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 = 9% of Principal

= 9% of $6200

= ⁹/₁₀₀ × 6200

= ^{9 × 6200}/₁₀₀

= ⁵⁵⁸⁰⁰/₁₀₀ = 558

Thus, simple Interest for 1 year = $558

Now,

∵ If the simple Interest is $558, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₅₅₈ years

∴ If the simple Interest is $3348, then the time = ¹/₅₅₈ × 3348 years

= ^{1 × 3348}/₅₅₈ years

= ³³⁴⁸/₅₅₈ = 6 years

Thus, time (T) = 6 years Answer

Similar Questions

(1) Charles took a loan of $5800 at the rate of 7% simple interest per annum. If he paid an amount of $8236 to clear the loan, then find the time period of the loan.

(2) Calculate the amount due after 9 years if Thomas borrowed a sum of $5800 at a rate of 4% simple interest.

(3) What amount does John have to pay after 5 years if he takes a loan of $3200 at 7% simple interest?

(4) Matthew took a loan of $6400 at the rate of 10% simple interest per annum. If he paid an amount of $12160 to clear the loan, then find the time period of the loan.

(5) Find the amount to be paid if Michael borrowed a sum of $5300 at 2% simple interest for 7 years.

(6) What amount will be due after 2 years if Thomas borrowed a sum of $3400 at a 8% simple interest?

(7) Find the amount to be paid if William borrowed a sum of $5500 at 4% simple interest for 8 years.

(8) Karen took a loan of $5900 at the rate of 10% simple interest per annum. If he paid an amount of $10620 to clear the loan, then find the time period of the loan.

(9) Matthew took a loan of $6400 at the rate of 8% simple interest per annum. If he paid an amount of $9984 to clear the loan, then find the time period of the loan.

(10) Calculate the amount due after 10 years if Joseph borrowed a sum of $5700 at a rate of 2% simple interest.