Simple Interest
Math MCQs

Question :    Karen took a loan of $5900 at the rate of 9% simple interest per annum. If he paid an amount of $9617 to clear the loan, then find the time period of the loan.

Correct Answer  7

Solution & Explanation

Solution

Given,

Principal (P) = $5900

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

Amount (A) = $9617

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 = $9617 – $5900 = $3717

Thus, Simple Interest = $3717

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 × 3717}/_{5900 × 9}

= ³⁷¹⁷⁰⁰/₅₃₁₀₀

= 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) = $5900

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

Simple Interest = $3717 (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 $5900

= ⁹/₁₀₀ × 5900

= ^{9 × 5900}/₁₀₀

= ⁵³¹⁰⁰/₁₀₀ = 531

Thus, simple Interest for 1 year = $531

Now,

∵ If the simple Interest is $531, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₅₃₁ years

∴ If the simple Interest is $3717, then the time = ¹/₅₃₁ × 3717 years

= ^{1 × 3717}/₅₃₁ years

= ³⁷¹⁷/₅₃₁ = 7 years

Thus, time (T) = 7 years Answer

Similar Questions

(1) Calculate the amount due after 9 years if Sarah borrowed a sum of $5850 at a rate of 4% simple interest.

(2) 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.

(3) Ashley had to pay $5096 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(4) Thomas took a loan of $5600 at the rate of 7% simple interest per annum. If he paid an amount of $8344 to clear the loan, then find the time period of the loan.

(5) Find the amount to be paid if Joseph borrowed a sum of $5700 at 3% simple interest for 8 years.

(6) Susan took a loan of $5300 at the rate of 7% simple interest per annum. If he paid an amount of $8268 to clear the loan, then find the time period of the loan.

(7) Jessica took a loan of $5500 at the rate of 7% simple interest per annum. If he paid an amount of $7810 to clear the loan, then find the time period of the loan.

(8) In how much time a principal of $3050 will amount to $3355 at a simple interest of 2% per annum?

(9) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 3% simple interest?

(10) How much loan did Margaret borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7620 to clear it?