Simple Interest
Math MCQs

Question :    Susan took a loan of $5300 at the rate of 7% simple interest per annum. If he paid an amount of $7897 to clear the loan, then find the time period of the loan.

Correct Answer  7

Solution & Explanation

Solution

Given,

Principal (P) = $5300

Rate of Simple Interest (R) = 7% per annum

Amount (A) = $7897

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 = $7897 – $5300 = $2597

Thus, Simple Interest = $2597

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 × 2597}/_{5300 × 7}

= ²⁵⁹⁷⁰⁰/₃₇₁₀₀

= 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) = $5300

Rate of Simple Interest (R) = 7% per annum

Simple Interest = $2597 (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 $5300

= ⁷/₁₀₀ × 5300

= ^{7 × 5300}/₁₀₀

= ³⁷¹⁰⁰/₁₀₀ = 371

Thus, simple Interest for 1 year = $371

Now,

∵ If the simple Interest is $371, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₃₇₁ years

∴ If the simple Interest is $2597, then the time = ¹/₃₇₁ × 2597 years

= ^{1 × 2597}/₃₇₁ years

= ²⁵⁹⁷/₃₇₁ = 7 years

Thus, time (T) = 7 years Answer

Similar Questions

(1) In how much time a principal of $3150 will amount to $3465 at a simple interest of 2% per annum?

(2) What amount does Barbara have to pay after 5 years if he takes a loan of $3550 at 4% simple interest?

(3) 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.

(4) Karen took a loan of $5900 at the rate of 8% simple interest per annum. If he paid an amount of $10620 to clear the loan, then find the time period of the loan.

(5) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 9% simple interest?

(6) If James borrowed $3000 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.

(7) Karen took a loan of $5900 at the rate of 9% simple interest per annum. If he paid an amount of $9086 to clear the loan, then find the time period of the loan.

(8) In how much time a principal of $3050 will amount to $3294 at a simple interest of 2% per annum?

(9) Calculate the amount due after 9 years if Jessica borrowed a sum of $5750 at a rate of 5% simple interest.

(10) What amount will be due after 2 years if Joshua borrowed a sum of $3950 at a 10% simple interest?