Simple Interest
Math MCQs

Question :    Thomas took a loan of $5600 at the rate of 8% simple interest per annum. If he paid an amount of $8736 to clear the loan, then find the time period of the loan.

Correct Answer  7

Solution & Explanation

Solution

Given,

Principal (P) = $5600

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

Amount (A) = $8736

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 = $8736 – $5600 = $3136

Thus, Simple Interest = $3136

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 × 3136}/_{5600 × 8}

= ³¹³⁶⁰⁰/₄₄₈₀₀

= 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) = $5600

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

Simple Interest = $3136 (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 $5600

= ⁸/₁₀₀ × 5600

= ^{8 × 5600}/₁₀₀

= ⁴⁴⁸⁰⁰/₁₀₀ = 448

Thus, simple Interest for 1 year = $448

Now,

∵ If the simple Interest is $448, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₄₈ years

∴ If the simple Interest is $3136, then the time = ¹/₄₄₈ × 3136 years

= ^{1 × 3136}/₄₄₈ years

= ³¹³⁶/₄₄₈ = 7 years

Thus, time (T) = 7 years Answer

Similar Questions

(1) Patricia took a loan of $4300 at the rate of 8% simple interest per annum. If he paid an amount of $6708 to clear the loan, then find the time period of the loan.

(2) If Sarah paid $4158 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(3) Sandra took a loan of $6900 at the rate of 10% simple interest per annum. If he paid an amount of $13110 to clear the loan, then find the time period of the loan.

(4) What amount will be due after 2 years if Kenneth borrowed a sum of $4000 at a 5% simple interest?

(5) Karen took a loan of $5900 at the rate of 6% simple interest per annum. If he paid an amount of $8378 to clear the loan, then find the time period of the loan.

(6) What amount does Jennifer have to pay after 6 years if he takes a loan of $3250 at 10% simple interest?

(7) Lisa took a loan of $6100 at the rate of 8% simple interest per annum. If he paid an amount of $9516 to clear the loan, then find the time period of the loan.

(8) Calculate the amount due if Linda borrowed a sum of $3350 at 5% simple interest for 4 years.

(9) How much loan did Thomas borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6670 to clear it?

(10) If Linda borrowed $3350 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.