Simple Interest
Math MCQs

Question :    Donald took a loan of $7000 at the rate of 6% simple interest per annum. If he paid an amount of $10360 to clear the loan, then find the time period of the loan.

Correct Answer  8

Solution & Explanation

Solution

Given,

Principal (P) = $7000

Rate of Simple Interest (R) = 6% per annum

Amount (A) = $10360

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 = $10360 – $7000 = $3360

Thus, Simple Interest = $3360

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 × 3360}/_{7000 × 6}

= ³³⁶⁰⁰⁰/₄₂₀₀₀

= 8 years (using formula)

Thus, Time (T) = 8 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) = $7000

Rate of Simple Interest (R) = 6% per annum

Simple Interest = $3360 (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 = 6% of Principal

= 6% of $7000

= ⁶/₁₀₀ × 7000

= ^{6 × 7000}/₁₀₀

= ⁴²⁰⁰⁰/₁₀₀ = 420

Thus, simple Interest for 1 year = $420

Now,

∵ If the simple Interest is $420, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₂₀ years

∴ If the simple Interest is $3360, then the time = ¹/₄₂₀ × 3360 years

= ^{1 × 3360}/₄₂₀ years

= ³³⁶⁰/₄₂₀ = 8 years

Thus, time (T) = 8 years Answer

Similar Questions

(1) Calculate the amount due if Patricia borrowed a sum of $3150 at 4% simple interest for 4 years.

(2) In how much time a principal of $3200 will amount to $3328 at a simple interest of 2% per annum?

(3) Michael took a loan of $4600 at the rate of 9% simple interest per annum. If he paid an amount of $8326 to clear the loan, then find the time period of the loan.

(4) In how much time a principal of $3100 will amount to $3286 at a simple interest of 3% per annum?

(5) Sarah had to pay $4312 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(6) In how much time a principal of $3000 will amount to $3480 at a simple interest of 4% per annum?

(7) Mark took a loan of $6800 at the rate of 10% simple interest per annum. If he paid an amount of $12920 to clear the loan, then find the time period of the loan.

(8) How much loan did Jeffrey borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9360 to clear it?

(9) If Mark paid $5280 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(10) Robert took a loan of $4200 at the rate of 10% simple interest per annum. If he paid an amount of $7560 to clear the loan, then find the time period of the loan.