Simple Interest
Math MCQs

Question :    Sarah took a loan of $5700 at the rate of 6% simple interest per annum. If he paid an amount of $8436 to clear the loan, then find the time period of the loan.

Correct Answer  8

Solution & Explanation

Solution

Given,

Principal (P) = $5700

Rate of Simple Interest (R) = 6% per annum

Amount (A) = $8436

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 = $8436 – $5700 = $2736

Thus, Simple Interest = $2736

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 × 2736}/_{5700 × 6}

= ²⁷³⁶⁰⁰/₃₄₂₀₀

= 8 years (using formula)

Thus, Time (T) = 8 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) = $5700

Rate of Simple Interest (R) = 6% per annum

Simple Interest = $2736 (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 = 6% of Principal

= 6% of $5700

= ⁶/₁₀₀ × 5700

= ^{6 × 5700}/₁₀₀

= ³⁴²⁰⁰/₁₀₀ = 342

Thus, simple Interest for 1 year = $342

Now,

∵ If the simple Interest is $342, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₃₄₂ years

∴ If the simple Interest is $2736, then the time = ¹/₃₄₂ × 2736 years

= ^{1 × 2736}/₃₄₂ years

= ²⁷³⁶/₃₄₂ = 8 years

Thus, time (T) = 8 years Answer

Similar Questions

(1) Sarah took a loan of $5700 at the rate of 9% simple interest per annum. If he paid an amount of $9291 to clear the loan, then find the time period of the loan.

(2) How much loan did Michael borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6625 to clear it?

(3) How much loan did Jessica borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6900 to clear it?

(4) How much loan did Deborah borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8940 to clear it?

(5) Find the amount to be paid if William borrowed a sum of $5500 at 9% simple interest for 7 years.

(6) Elizabeth took a loan of $4900 at the rate of 6% simple interest per annum. If he paid an amount of $6664 to clear the loan, then find the time period of the loan.

(7) How much loan did Edward borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9500 to clear it?

(8) Linda took a loan of $4700 at the rate of 6% simple interest per annum. If he paid an amount of $6956 to clear the loan, then find the time period of the loan.

(9) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 9% simple interest?

(10) Calculate the amount due if Sarah borrowed a sum of $3850 at 2% simple interest for 3 years.