Simple Interest
Math MCQs

Question :    Richard took a loan of $5200 at the rate of 9% simple interest per annum. If he paid an amount of $9412 to clear the loan, then find the time period of the loan.

Correct Answer  9

Solution & Explanation

Solution

Given,

Principal (P) = $5200

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

Amount (A) = $9412

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 = $9412 – $5200 = $4212

Thus, Simple Interest = $4212

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 × 4212}/_{5200 × 9}

= ⁴²¹²⁰⁰/₄₆₈₀₀

= 9 years (using formula)

Thus, Time (T) = 9 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) = $5200

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

Simple Interest = $4212 (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 $5200

= ⁹/₁₀₀ × 5200

= ^{9 × 5200}/₁₀₀

= ⁴⁶⁸⁰⁰/₁₀₀ = 468

Thus, simple Interest for 1 year = $468

Now,

∵ If the simple Interest is $468, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₆₈ years

∴ If the simple Interest is $4212, then the time = ¹/₄₆₈ × 4212 years

= ^{1 × 4212}/₄₆₈ years

= ⁴²¹²/₄₆₈ = 9 years

Thus, time (T) = 9 years Answer

Similar Questions

(1) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 10% simple interest?

(2) What amount does David have to pay after 5 years if he takes a loan of $3400 at 6% simple interest?

(3) What amount will be due after 2 years if Matthew borrowed a sum of $3600 at a 8% simple interest?

(4) Calculate the amount due if Christopher borrowed a sum of $4000 at 6% simple interest for 4 years.

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

(6) Sarah took a loan of $5700 at the rate of 9% simple interest per annum. If he paid an amount of $9804 to clear the loan, then find the time period of the loan.

(7) How much loan did Timothy borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8510 to clear it?

(8) Find the amount to be paid if Mary borrowed a sum of $5050 at 8% simple interest for 8 years.

(9) If Michelle paid $5742 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(10) Jennifer took a loan of $4500 at the rate of 10% simple interest per annum. If he paid an amount of $8100 to clear the loan, then find the time period of the loan.