Simple Interest
Math MCQs

Question :    James took a loan of $4000 at the rate of 6% simple interest per annum. If he paid an amount of $6160 to clear the loan, then find the time period of the loan.

Correct Answer  9

Solution & Explanation

Solution

Given,

Principal (P) = $4000

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

Amount (A) = $6160

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 = $6160 – $4000 = $2160

Thus, Simple Interest = $2160

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 × 2160}/_{4000 × 6}

= ²¹⁶⁰⁰⁰/₂₄₀₀₀

= 9 years (using formula)

Thus, Time (T) = 9 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) = $4000

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

Simple Interest = $2160 (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 $4000

= ⁶/₁₀₀ × 4000

= ^{6 × 4000}/₁₀₀

= ²⁴⁰⁰⁰/₁₀₀ = 240

Thus, simple Interest for 1 year = $240

Now,

∵ If the simple Interest is $240, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₂₄₀ years

∴ If the simple Interest is $2160, then the time = ¹/₂₄₀ × 2160 years

= ^{1 × 2160}/₂₄₀ years

= ²¹⁶⁰/₂₄₀ = 9 years

Thus, time (T) = 9 years Answer

Similar Questions

(1) Joseph took a loan of $5400 at the rate of 8% simple interest per annum. If he paid an amount of $9288 to clear the loan, then find the time period of the loan.

(2) Joseph took a loan of $5400 at the rate of 7% simple interest per annum. If he paid an amount of $7668 to clear the loan, then find the time period of the loan.

(3) What amount does David have to pay after 6 years if he takes a loan of $3400 at 9% simple interest?

(4) Calculate the amount due if Mary borrowed a sum of $3050 at 6% simple interest for 4 years.

(5) Barbara took a loan of $5100 at the rate of 10% simple interest per annum. If he paid an amount of $9690 to clear the loan, then find the time period of the loan.

(6) How much loan did Kevin borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8875 to clear it?

(7) Richard took a loan of $5200 at the rate of 7% simple interest per annum. If he paid an amount of $8840 to clear the loan, then find the time period of the loan.

(8) What amount will be due after 2 years if Steven borrowed a sum of $3800 at a 8% simple interest?

(9) What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 3% simple interest?

(10) If Emily paid $5130 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.