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 $5920 to clear the loan, then find the time period of the loan.

Correct Answer  8

Solution & Explanation

Solution

Given,

Principal (P) = $4000

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

Amount (A) = $5920

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 = $5920 – $4000 = $1920

Thus, Simple Interest = $1920

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 × 1920}/_{4000 × 6}

= ¹⁹²⁰⁰⁰/₂₄₀₀₀

= 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) = $4000

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

Simple Interest = $1920 (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 $1920, then the time = ¹/₂₄₀ × 1920 years

= ^{1 × 1920}/₂₄₀ years

= ¹⁹²⁰/₂₄₀ = 8 years

Thus, time (T) = 8 years Answer

Similar Questions

(1) Anthony took a loan of $6600 at the rate of 7% simple interest per annum. If he paid an amount of $10758 to clear the loan, then find the time period of the loan.

(2) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 9% simple interest?

(3) Barbara took a loan of $5100 at the rate of 9% simple interest per annum. If he paid an amount of $9690 to clear the loan, then find the time period of the loan.

(4) What amount does William have to pay after 5 years if he takes a loan of $3500 at 8% simple interest?

(5) Betty had to pay $4887.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(6) How much loan did Deborah borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8195 to clear it?

(7) Thomas took a loan of $5600 at the rate of 8% simple interest per annum. If he paid an amount of $9632 to clear the loan, then find the time period of the loan.

(8) If Elizabeth paid $4140 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 Mary borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $5807.5 to clear it?

(10) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 10% simple interest for 3 years.