Simple Interest
Math MCQs

Question :    Thomas took a loan of $5600 at the rate of 6% simple interest per annum. If he paid an amount of $8624 to clear the loan, then find the time period of the loan.

Correct Answer  9

Solution & Explanation

Solution

Given,

Principal (P) = $5600

Rate of Simple Interest (R) = 6% per annum

Amount (A) = $8624

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 = $8624 – $5600 = $3024

Thus, Simple Interest = $3024

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 × 3024}/_{5600 × 6}

= ³⁰²⁴⁰⁰/₃₃₆₀₀

= 9 years (using formula)

Thus, Time (T) = 9 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) = $5600

Rate of Simple Interest (R) = 6% per annum

Simple Interest = $3024 (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 = 6% of Principal

= 6% of $5600

= ⁶/₁₀₀ × 5600

= ^{6 × 5600}/₁₀₀

= ³³⁶⁰⁰/₁₀₀ = 336

Thus, simple Interest for 1 year = $336

Now,

∵ If the simple Interest is $336, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₃₃₆ years

∴ If the simple Interest is $3024, then the time = ¹/₃₃₆ × 3024 years

= ^{1 × 3024}/₃₃₆ years

= ³⁰²⁴/₃₃₆ = 9 years

Thus, time (T) = 9 years Answer

Similar Questions

(1) What amount does Jessica have to pay after 6 years if he takes a loan of $3750 at 8% simple interest?

(2) Ashley had to pay $4823 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(3) What amount does Thomas have to pay after 5 years if he takes a loan of $3800 at 4% simple interest?

(4) Calculate the amount due after 10 years if Robert borrowed a sum of $5100 at a rate of 10% simple interest.

(5) Susan took a loan of $5300 at the rate of 8% simple interest per annum. If he paid an amount of $8268 to clear the loan, then find the time period of the loan.

(6) What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 9% simple interest?

(7) What amount does Patricia have to pay after 6 years if he takes a loan of $3150 at 10% simple interest?

(8) How much loan did Ashley borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8187.5 to clear it?

(9) Calculate the amount due if James borrowed a sum of $3000 at 7% simple interest for 3 years.

(10) David took a loan of $4800 at the rate of 6% simple interest per annum. If he paid an amount of $6528 to clear the loan, then find the time period of the loan.