Simple Interest
Math MCQs

Question :    Susan took a loan of $5300 at the rate of 9% simple interest per annum. If he paid an amount of $8162 to clear the loan, then find the time period of the loan.

Correct Answer  6

Solution & Explanation

Solution

Given,

Principal (P) = $5300

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

Amount (A) = $8162

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 = $8162 – $5300 = $2862

Thus, Simple Interest = $2862

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 × 2862}/_{5300 × 9}

= ²⁸⁶²⁰⁰/₄₇₇₀₀

= 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) = $5300

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

Simple Interest = $2862 (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 $5300

= ⁹/₁₀₀ × 5300

= ^{9 × 5300}/₁₀₀

= ⁴⁷⁷⁰⁰/₁₀₀ = 477

Thus, simple Interest for 1 year = $477

Now,

∵ If the simple Interest is $477, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₇₇ years

∴ If the simple Interest is $2862, then the time = ¹/₄₇₇ × 2862 years

= ^{1 × 2862}/₄₇₇ years

= ²⁸⁶²/₄₇₇ = 6 years

Thus, time (T) = 6 years Answer

Similar Questions

(1) Calculate the amount due if Thomas borrowed a sum of $3800 at 2% simple interest for 3 years.

(2) Calculate the amount due if Robert borrowed a sum of $3100 at 5% simple interest for 4 years.

(3) Calculate the amount due if Susan borrowed a sum of $3650 at 6% simple interest for 3 years.

(4) Ashley had to pay $4823 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(5) Joseph took a loan of $5400 at the rate of 8% simple interest per annum. If he paid an amount of $9288 to clear the loan, then find the time period of the loan.

(6) Calculate the amount due if Susan borrowed a sum of $3650 at 5% simple interest for 4 years.

(7) What amount will be due after 2 years if Thomas borrowed a sum of $3400 at a 4% simple interest?

(8) How much loan did Kenneth borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7700 to clear it?

(9) Find the amount to be paid if David borrowed a sum of $5400 at 3% simple interest for 8 years.

(10) If Kimberly paid $5022 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.