Simple Interest
Math MCQs

Question :    Sarah took a loan of $5700 at the rate of 8% simple interest per annum. If he paid an amount of $8892 to clear the loan, then find the time period of the loan.

Correct Answer  7

Solution & Explanation

Solution

Given,

Principal (P) = $5700

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

Amount (A) = $8892

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 = $8892 – $5700 = $3192

Thus, Simple Interest = $3192

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 × 3192}/_{5700 × 8}

= ³¹⁹²⁰⁰/₄₅₆₀₀

= 7 years (using formula)

Thus, Time (T) = 7 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) = 8% per annum

Simple Interest = $3192 (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 $5700

= ⁸/₁₀₀ × 5700

= ^{8 × 5700}/₁₀₀

= ⁴⁵⁶⁰⁰/₁₀₀ = 456

Thus, simple Interest for 1 year = $456

Now,

∵ If the simple Interest is $456, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₅₆ years

∴ If the simple Interest is $3192, then the time = ¹/₄₅₆ × 3192 years

= ^{1 × 3192}/₄₅₆ years

= ³¹⁹²/₄₅₆ = 7 years

Thus, time (T) = 7 years Answer

Similar Questions

(1) Calculate the amount due if Patricia borrowed a sum of $3150 at 2% simple interest for 3 years.

(2) Find the amount to be paid if James borrowed a sum of $5000 at 8% simple interest for 7 years.

(3) How much loan did Deborah borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8195 to clear it?

(4) David took a loan of $4800 at the rate of 10% simple interest per annum. If he paid an amount of $8160 to clear the loan, then find the time period of the loan.

(5) What amount does Barbara have to pay after 5 years if he takes a loan of $3550 at 5% simple interest?

(6) If Mary paid $3416 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(7) How much loan did Anthony borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7245 to clear it?

(8) How much loan did Lisa borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6655 to clear it?

(9) Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 7% simple interest.

(10) Calculate the amount due if Richard borrowed a sum of $3600 at 9% simple interest for 4 years.