Simple Interest
Math MCQs

Question :    Karen took a loan of $5900 at the rate of 9% simple interest per annum. If he paid an amount of $9086 to clear the loan, then find the time period of the loan.

Correct Answer  6

Solution & Explanation

Solution

Given,

Principal (P) = $5900

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

Amount (A) = $9086

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 = $9086 – $5900 = $3186

Thus, Simple Interest = $3186

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 × 3186}/_{5900 × 9}

= ³¹⁸⁶⁰⁰/₅₃₁₀₀

= 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) = $5900

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

Simple Interest = $3186 (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 $5900

= ⁹/₁₀₀ × 5900

= ^{9 × 5900}/₁₀₀

= ⁵³¹⁰⁰/₁₀₀ = 531

Thus, simple Interest for 1 year = $531

Now,

∵ If the simple Interest is $531, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₅₃₁ years

∴ If the simple Interest is $3186, then the time = ¹/₅₃₁ × 3186 years

= ^{1 × 3186}/₅₃₁ years

= ³¹⁸⁶/₅₃₁ = 6 years

Thus, time (T) = 6 years Answer

Similar Questions

(1) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 3% simple interest?

(2) Robert took a loan of $4200 at the rate of 8% simple interest per annum. If he paid an amount of $7224 to clear the loan, then find the time period of the loan.

(3) John took a loan of $4400 at the rate of 6% simple interest per annum. If he paid an amount of $7040 to clear the loan, then find the time period of the loan.

(4) Calculate the amount due if Jennifer borrowed a sum of $3250 at 8% simple interest for 3 years.

(5) What amount does Thomas have to pay after 6 years if he takes a loan of $3800 at 6% simple interest?

(6) If Elizabeth paid $4140 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(7) Calculate the amount due if Jessica borrowed a sum of $3750 at 10% simple interest for 4 years.

(8) Mark took a loan of $6800 at the rate of 10% simple interest per annum. If he paid an amount of $11560 to clear the loan, then find the time period of the loan.

(9) How much loan did Kenneth borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8400 to clear it?

(10) Calculate the amount due if Patricia borrowed a sum of $3150 at 8% simple interest for 4 years.