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) Thomas took a loan of $5600 at the rate of 10% simple interest per annum. If he paid an amount of $10080 to clear the loan, then find the time period of the loan.

(2) What amount does John have to pay after 5 years if he takes a loan of $3200 at 7% simple interest?

(3) Mary took a loan of $4100 at the rate of 7% simple interest per annum. If he paid an amount of $6396 to clear the loan, then find the time period of the loan.

(4) Patricia had to pay $3433.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(5) If Richard paid $4176 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(6) If Jennifer paid $3510 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(7) Thomas took a loan of $5600 at the rate of 7% simple interest per annum. If he paid an amount of $9128 to clear the loan, then find the time period of the loan.

(8) Calculate the amount due if Karen borrowed a sum of $3950 at 7% simple interest for 3 years.

(9) Find the amount to be paid if Patricia borrowed a sum of $5150 at 4% simple interest for 8 years.

(10) Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 4% simple interest.