Simple Interest
Math MCQs

Question :    Christopher took a loan of $6000 at the rate of 10% simple interest per annum. If he paid an amount of $10800 to clear the loan, then find the time period of the loan.

Correct Answer  8

Solution & Explanation

Solution

Given,

Principal (P) = $6000

Rate of Simple Interest (R) = 10% per annum

Amount (A) = $10800

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 = $10800 – $6000 = $4800

Thus, Simple Interest = $4800

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 × 4800}/_{6000 × 10}

= ⁴⁸⁰⁰⁰⁰/₆₀₀₀₀

= 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) = $6000

Rate of Simple Interest (R) = 10% per annum

Simple Interest = $4800 (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 = 10% of Principal

= 10% of $6000

= ¹⁰/₁₀₀ × 6000

= ^{10 × 6000}/₁₀₀

= ⁶⁰⁰⁰⁰/₁₀₀ = 600

Thus, simple Interest for 1 year = $600

Now,

∵ If the simple Interest is $600, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₆₀₀ years

∴ If the simple Interest is $4800, then the time = ¹/₆₀₀ × 4800 years

= ^{1 × 4800}/₆₀₀ years

= ⁴⁸⁰⁰/₆₀₀ = 8 years

Thus, time (T) = 8 years Answer

Similar Questions

(1) Linda had to pay $3651.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(2) Calculate the amount due after 9 years if John borrowed a sum of $5200 at a rate of 10% simple interest.

(3) Calculate the amount due after 9 years if Michael borrowed a sum of $5300 at a rate of 8% simple interest.

(4) Elizabeth had to pay $3864 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(5) What amount does John have to pay after 5 years if he takes a loan of $3200 at 2% simple interest?

(6) How much loan did Donna borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7877.5 to clear it?

(7) Joseph took a loan of $5400 at the rate of 10% simple interest per annum. If he paid an amount of $9180 to clear the loan, then find the time period of the loan.

(8) If Jennifer paid $3640 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(9) Margaret took a loan of $6700 at the rate of 7% simple interest per annum. If he paid an amount of $9514 to clear the loan, then find the time period of the loan.

(10) Find the amount to be paid if Linda borrowed a sum of $5350 at 4% simple interest for 7 years.