Simple Interest
Math MCQs

Question :    William took a loan of $5000 at the rate of 6% simple interest per annum. If he paid an amount of $6800 to clear the loan, then find the time period of the loan.

Correct Answer  6

Solution & Explanation

Solution

Given,

Principal (P) = $5000

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

Amount (A) = $6800

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 = $6800 – $5000 = $1800

Thus, Simple Interest = $1800

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 × 1800}/_{5000 × 6}

= ¹⁸⁰⁰⁰⁰/₃₀₀₀₀

= 6 years (using formula)

Thus, Time (T) = 6 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) = $5000

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

Simple Interest = $1800 (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 $5000

= ⁶/₁₀₀ × 5000

= ^{6 × 5000}/₁₀₀

= ³⁰⁰⁰⁰/₁₀₀ = 300

Thus, simple Interest for 1 year = $300

Now,

∵ If the simple Interest is $300, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₃₀₀ years

∴ If the simple Interest is $1800, then the time = ¹/₃₀₀ × 1800 years

= ^{1 × 1800}/₃₀₀ years

= ¹⁸⁰⁰/₃₀₀ = 6 years

Thus, time (T) = 6 years Answer

Similar Questions

(1) 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.

(2) Joseph took a loan of $5400 at the rate of 9% simple interest per annum. If he paid an amount of $9288 to clear the loan, then find the time period of the loan.

(3) What amount does Mary have to pay after 5 years if he takes a loan of $3050 at 10% simple interest?

(4) Patricia took a loan of $4300 at the rate of 8% simple interest per annum. If he paid an amount of $7740 to clear the loan, then find the time period of the loan.

(5) Daniel took a loan of $6200 at the rate of 10% simple interest per annum. If he paid an amount of $11780 to clear the loan, then find the time period of the loan.

(6) How much loan did John borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6240 to clear it?

(7) Patricia took a loan of $4300 at the rate of 10% simple interest per annum. If he paid an amount of $8600 to clear the loan, then find the time period of the loan.

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

(9) Susan took a loan of $5300 at the rate of 10% simple interest per annum. If he paid an amount of $10600 to clear the loan, then find the time period of the loan.

(10) Calculate the amount due if Barbara borrowed a sum of $3550 at 3% simple interest for 3 years.