Simple Interest
Math MCQs

Question :    Sarah took a loan of $5700 at the rate of 9% simple interest per annum. If he paid an amount of $8778 to clear the loan, then find the time period of the loan.

Correct Answer  6

Solution & Explanation

Solution

Given,

Principal (P) = $5700

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

Amount (A) = $8778

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 = $8778 – $5700 = $3078

Thus, Simple Interest = $3078

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 × 3078}/_{5700 × 9}

= ³⁰⁷⁸⁰⁰/₅₁₃₀₀

= 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) = $5700

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

Simple Interest = $3078 (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 $5700

= ⁹/₁₀₀ × 5700

= ^{9 × 5700}/₁₀₀

= ⁵¹³⁰⁰/₁₀₀ = 513

Thus, simple Interest for 1 year = $513

Now,

∵ If the simple Interest is $513, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₅₁₃ years

∴ If the simple Interest is $3078, then the time = ¹/₅₁₃ × 3078 years

= ^{1 × 3078}/₅₁₃ years

= ³⁰⁷⁸/₅₁₃ = 6 years

Thus, time (T) = 6 years Answer

Similar Questions

(1) Matthew took a loan of $6400 at the rate of 9% simple interest per annum. If he paid an amount of $10432 to clear the loan, then find the time period of the loan.

(2) Mark took a loan of $6800 at the rate of 10% simple interest per annum. If he paid an amount of $12240 to clear the loan, then find the time period of the loan.

(3) Patricia took a loan of $4300 at the rate of 9% simple interest per annum. If he paid an amount of $6622 to clear the loan, then find the time period of the loan.

(4) Thomas took a loan of $5600 at the rate of 9% simple interest per annum. If he paid an amount of $9632 to clear the loan, then find the time period of the loan.

(5) What amount does Karen have to pay after 5 years if he takes a loan of $3950 at 9% simple interest?

(6) Find the amount to be paid if William borrowed a sum of $5500 at 5% simple interest for 8 years.

(7) Calculate the amount due after 9 years if Sarah borrowed a sum of $5850 at a rate of 2% simple interest.

(8) Nancy took a loan of $6300 at the rate of 7% simple interest per annum. If he paid an amount of $9828 to clear the loan, then find the time period of the loan.

(9) What amount will be due after 2 years if Charles borrowed a sum of $3450 at a 5% simple interest?

(10) Calculate the amount due if Christopher borrowed a sum of $4000 at 3% simple interest for 3 years.