Simple Interest
Math MCQs

Question :    Betty took a loan of $6500 at the rate of 8% simple interest per annum. If he paid an amount of $10140 to clear the loan, then find the time period of the loan.

Correct Answer  7

Solution & Explanation

Solution

Given,

Principal (P) = $6500

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

Amount (A) = $10140

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 = $10140 – $6500 = $3640

Thus, Simple Interest = $3640

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 × 3640}/_{6500 × 8}

= ³⁶⁴⁰⁰⁰/₅₂₀₀₀

= 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) = $6500

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

Simple Interest = $3640 (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 $6500

= ⁸/₁₀₀ × 6500

= ^{8 × 6500}/₁₀₀

= ⁵²⁰⁰⁰/₁₀₀ = 520

Thus, simple Interest for 1 year = $520

Now,

∵ If the simple Interest is $520, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₅₂₀ years

∴ If the simple Interest is $3640, then the time = ¹/₅₂₀ × 3640 years

= ^{1 × 3640}/₅₂₀ years

= ³⁶⁴⁰/₅₂₀ = 7 years

Thus, time (T) = 7 years Answer

Similar Questions

(1) How much loan did Thomas borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6960 to clear it?

(2) Daniel took a loan of $6200 at the rate of 8% simple interest per annum. If he paid an amount of $11160 to clear the loan, then find the time period of the loan.

(3) Elizabeth took a loan of $4900 at the rate of 6% simple interest per annum. If he paid an amount of $7840 to clear the loan, then find the time period of the loan.

(4) How much loan did Paul borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7370 to clear it?

(5) Matthew took a loan of $6400 at the rate of 9% simple interest per annum. If he paid an amount of $11584 to clear the loan, then find the time period of the loan.

(6) If Nancy paid $4980 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(7) Richard took a loan of $5200 at the rate of 8% simple interest per annum. If he paid an amount of $7696 to clear the loan, then find the time period of the loan.

(8) Calculate the amount due after 10 years if Robert borrowed a sum of $5100 at a rate of 2% simple interest.

(9) Thomas took a loan of $5600 at the rate of 9% simple interest per annum. If he paid an amount of $10136 to clear the loan, then find the time period of the loan.

(10) What amount will be due after 2 years if Paul borrowed a sum of $3850 at a 9% simple interest?