Simple Interest
Math MCQs

Question :    Daniel took a loan of $6200 at the rate of 10% simple interest per annum. If he paid an amount of $11160 to clear the loan, then find the time period of the loan.

Correct Answer  8

Solution & Explanation

Solution

Given,

Principal (P) = $6200

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

Amount (A) = $11160

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 = $11160 – $6200 = $4960

Thus, Simple Interest = $4960

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 × 4960}/_{6200 × 10}

= ⁴⁹⁶⁰⁰⁰/₆₂₀₀₀

= 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) = $6200

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

Simple Interest = $4960 (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 $6200

= ¹⁰/₁₀₀ × 6200

= ^{10 × 6200}/₁₀₀

= ⁶²⁰⁰⁰/₁₀₀ = 620

Thus, simple Interest for 1 year = $620

Now,

∵ If the simple Interest is $620, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₆₂₀ years

∴ If the simple Interest is $4960, then the time = ¹/₆₂₀ × 4960 years

= ^{1 × 4960}/₆₂₀ years

= ⁴⁹⁶⁰/₆₂₀ = 8 years

Thus, time (T) = 8 years Answer

Similar Questions

(1) Patricia had to pay $3339 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(2) Christopher took a loan of $6000 at the rate of 7% simple interest per annum. If he paid an amount of $8940 to clear the loan, then find the time period of the loan.

(3) How much loan did Kenneth borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8050 to clear it?

(4) Calculate the amount due after 10 years if Karen borrowed a sum of $5950 at a rate of 8% simple interest.

(5) Calculate the amount due if Joseph borrowed a sum of $3700 at 6% simple interest for 4 years.

(6) David took a loan of $4800 at the rate of 10% simple interest per annum. If he paid an amount of $8160 to clear the loan, then find the time period of the loan.

(7) James took a loan of $4000 at the rate of 6% simple interest per annum. If he paid an amount of $5680 to clear the loan, then find the time period of the loan.

(8) If Christopher paid $4800 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(9) How much loan did Deborah borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8940 to clear it?

(10) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 5% simple interest for 8 years.