Simple Interest
Math MCQs

Question :    Charles took a loan of $5800 at the rate of 9% simple interest per annum. If he paid an amount of $9976 to clear the loan, then find the time period of the loan.

Correct Answer  8

Solution & Explanation

Solution

Given,

Principal (P) = $5800

Rate of Simple Interest (R) = 9% per annum

Amount (A) = $9976

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 = $9976 – $5800 = $4176

Thus, Simple Interest = $4176

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 × 4176}/_{5800 × 9}

= ⁴¹⁷⁶⁰⁰/₅₂₂₀₀

= 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) = $5800

Rate of Simple Interest (R) = 9% per annum

Simple Interest = $4176 (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 = 9% of Principal

= 9% of $5800

= ⁹/₁₀₀ × 5800

= ^{9 × 5800}/₁₀₀

= ⁵²²⁰⁰/₁₀₀ = 522

Thus, simple Interest for 1 year = $522

Now,

∵ If the simple Interest is $522, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₅₂₂ years

∴ If the simple Interest is $4176, then the time = ¹/₅₂₂ × 4176 years

= ^{1 × 4176}/₅₂₂ years

= ⁴¹⁷⁶/₅₂₂ = 8 years

Thus, time (T) = 8 years Answer

Similar Questions

(1) John took a loan of $4400 at the rate of 8% simple interest per annum. If he paid an amount of $6864 to clear the loan, then find the time period of the loan.

(2) Calculate the amount due if Linda borrowed a sum of $3350 at 2% simple interest for 3 years.

(3) Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 3% simple interest.

(4) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 10% simple interest?

(5) If Richard paid $4320 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(6) Matthew took a loan of $6400 at the rate of 9% simple interest per annum. If he paid an amount of $9856 to clear the loan, then find the time period of the loan.

(7) How much loan did Michelle borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8340 to clear it?

(8) Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 9% simple interest.

(9) Margaret took a loan of $6700 at the rate of 7% simple interest per annum. If he paid an amount of $9514 to clear the loan, then find the time period of the loan.

(10) Calculate the amount due if David borrowed a sum of $3400 at 10% simple interest for 4 years.