Simple Interest
Math MCQs

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

Correct Answer  10

Solution & Explanation

Solution

Given,

Principal (P) = $5900

Rate of Simple Interest (R) = 8% per annum

Amount (A) = $10620

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 = $10620 – $5900 = $4720

Thus, Simple Interest = $4720

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 × 4720}/_{5900 × 8}

= ⁴⁷²⁰⁰⁰/₄₇₂₀₀

= 10 years (using formula)

Thus, Time (T) = 10 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) = 8% per annum

Simple Interest = $4720 (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 $5900

= ⁸/₁₀₀ × 5900

= ^{8 × 5900}/₁₀₀

= ⁴⁷²⁰⁰/₁₀₀ = 472

Thus, simple Interest for 1 year = $472

Now,

∵ If the simple Interest is $472, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₇₂ years

∴ If the simple Interest is $4720, then the time = ¹/₄₇₂ × 4720 years

= ^{1 × 4720}/₄₇₂ years

= ⁴⁷²⁰/₄₇₂ = 10 years

Thus, time (T) = 10 years Answer

Similar Questions

(1) What amount will be due after 2 years if Robert borrowed a sum of $3050 at a 8% simple interest?

(2) Karen took a loan of $5900 at the rate of 6% simple interest per annum. If he paid an amount of $8378 to clear the loan, then find the time period of the loan.

(3) Calculate the amount due after 10 years if Thomas borrowed a sum of $5800 at a rate of 10% simple interest.

(4) Find the amount to be paid if Linda borrowed a sum of $5350 at 7% simple interest for 8 years.

(5) Elizabeth took a loan of $4900 at the rate of 9% simple interest per annum. If he paid an amount of $9310 to clear the loan, then find the time period of the loan.

(6) Margaret took a loan of $6700 at the rate of 6% simple interest per annum. If he paid an amount of $9916 to clear the loan, then find the time period of the loan.

(7) How much loan did Sharon borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8525 to clear it?

(8) Find the amount to be paid if Patricia borrowed a sum of $5150 at 4% simple interest for 7 years.

(9) Calculate the amount due if Mary borrowed a sum of $3050 at 9% simple interest for 4 years.

(10) Find the amount to be paid if Thomas borrowed a sum of $5800 at 9% simple interest for 8 years.