Simple Interest
Math MCQs

Question :    Richard took a loan of $5200 at the rate of 8% simple interest per annum. If he paid an amount of $8944 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) = 8% per annum

Amount (A) = $8944

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 = $8944 – $5200 = $3744

Thus, Simple Interest = $3744

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 × 3744}/_{5200 × 8}

= ³⁷⁴⁴⁰⁰/₄₁₆₀₀

= 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) = 8% per annum

Simple Interest = $3744 (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 $5200

= ⁸/₁₀₀ × 5200

= ^{8 × 5200}/₁₀₀

= ⁴¹⁶⁰⁰/₁₀₀ = 416

Thus, simple Interest for 1 year = $416

Now,

∵ If the simple Interest is $416, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₁₆ years

∴ If the simple Interest is $3744, then the time = ¹/₄₁₆ × 3744 years

= ^{1 × 3744}/₄₁₆ years

= ³⁷⁴⁴/₄₁₆ = 9 years

Thus, time (T) = 9 years Answer

Similar Questions

(1) Michael took a loan of $4600 at the rate of 7% simple interest per annum. If he paid an amount of $7176 to clear the loan, then find the time period of the loan.

(2) What amount does Jessica have to pay after 5 years if he takes a loan of $3750 at 8% simple interest?

(3) How much loan did Jeffrey borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9750 to clear it?

(4) William took a loan of $5000 at the rate of 6% simple interest per annum. If he paid an amount of $7400 to clear the loan, then find the time period of the loan.

(5) In how much time a principal of $3050 will amount to $3172 at a simple interest of 2% per annum?

(6) Calculate the amount due after 9 years if Jessica borrowed a sum of $5750 at a rate of 4% simple interest.

(7) Calculate the amount due if Jennifer borrowed a sum of $3250 at 8% simple interest for 4 years.

(8) Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 9% simple interest.

(9) Joshua had to pay $5194 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(10) What amount does Elizabeth have to pay after 6 years if he takes a loan of $3450 at 3% simple interest?