Simple Interest
MCQs Math

Question:     Sarah took a loan of $5700 at the rate of 7% 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  10

Solution And Explanation

Solution

Given,

Principal (P) = $5700

Rate of Simple Interest (R) = 7% 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 × 7}

= ³⁹⁹⁰⁰⁰/₃₉₉₀₀

= 10 years (using formula)

Thus, Time (T) = 10 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) = 7% 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 = 7% of Principal

= 7% of $5700

= ⁷/₁₀₀ × 5700

= ^{7 × 5700}/₁₀₀

= ³⁹⁹⁰⁰/₁₀₀ = 399

Thus, simple Interest for 1 year = $399

Now,

∵ If the simple Interest is $399, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₃₉₉ years

∴ If the simple Interest is $3990, then the time = ¹/₃₉₉ × 3990 years

= ^{1 × 3990}/₃₉₉ years

= ³⁹⁹⁰/₃₉₉ = 10 years

Thus, time (T) = 10 years Answer

Similar Questions

(1) How much loan did Cynthia borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $9142.5 to clear it?

(2) What amount will be due after 2 years if Kenneth borrowed a sum of $4000 at a 9% simple interest?

(3) Find the amount to be paid if Sarah borrowed a sum of $5850 at 3% simple interest for 8 years.

(4) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 7% simple interest?

(5) If Barbara borrowed $3550 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.

(6) James took a loan of $4000 at the rate of 8% simple interest per annum. If he paid an amount of $7200 to clear the loan, then find the time period of the loan.

(7) Find the amount to be paid if Christopher borrowed a sum of $6000 at 7% simple interest for 7 years.

(8) What amount does David have to pay after 5 years if he takes a loan of $3400 at 7% simple interest?

(9) Calculate the amount due if Jessica borrowed a sum of $3750 at 4% simple interest for 3 years.

(10) How much loan did Daniel borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7625 to clear it?