Simple Interest
Math MCQs

Question :    Sarah took a loan of $5700 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.

Correct Answer  7

Solution & Explanation

Solution

Given,

Principal (P) = $5700

Rate of Simple Interest (R) = 10% per annum

Amount (A) = $9690

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 = $9690 – $5700 = $3990

Thus, Simple Interest = $3990

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 × 3990}/_{5700 × 10}

= ³⁹⁹⁰⁰⁰/₅₇₀₀₀

= 7 years (using formula)

Thus, Time (T) = 7 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) = $5700

Rate of Simple Interest (R) = 10% per annum

Simple Interest = $3990 (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 = 10% of Principal

= 10% of $5700

= ¹⁰/₁₀₀ × 5700

= ^{10 × 5700}/₁₀₀

= ⁵⁷⁰⁰⁰/₁₀₀ = 570

Thus, simple Interest for 1 year = $570

Now,

∵ If the simple Interest is $570, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₅₇₀ years

∴ If the simple Interest is $3990, then the time = ¹/₅₇₀ × 3990 years

= ^{1 × 3990}/₅₇₀ years

= ³⁹⁹⁰/₅₇₀ = 7 years

Thus, time (T) = 7 years Answer

Similar Questions

(1) Calculate the amount due after 10 years if Richard borrowed a sum of $5600 at a rate of 5% simple interest.

(2) Jessica took a loan of $5500 at the rate of 10% simple interest per annum. If he paid an amount of $9350 to clear the loan, then find the time period of the loan.

(3) Jennifer took a loan of $4500 at the rate of 9% simple interest per annum. If he paid an amount of $6930 to clear the loan, then find the time period of the loan.

(4) Find the amount to be paid if Patricia borrowed a sum of $5150 at 10% simple interest for 7 years.

(5) If Mary paid $3660 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(6) Charles took a loan of $5800 at the rate of 8% simple interest per annum. If he paid an amount of $9512 to clear the loan, then find the time period of the loan.

(7) John took a loan of $4400 at the rate of 6% simple interest per annum. If he paid an amount of $6776 to clear the loan, then find the time period of the loan.

(8) Calculate the amount due after 10 years if John borrowed a sum of $5200 at a rate of 5% simple interest.

(9) What amount will be due after 2 years if Joshua borrowed a sum of $3950 at a 5% simple interest?

(10) Find the amount to be paid if Joseph borrowed a sum of $5700 at 8% simple interest for 7 years.