Simple Interest
Math MCQs

Question :    Linda took a loan of $4700 at the rate of 7% simple interest per annum. If he paid an amount of $7003 to clear the loan, then find the time period of the loan.

Correct Answer  7

Solution & Explanation

Solution

Given,

Principal (P) = $4700

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

Amount (A) = $7003

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 = $7003 – $4700 = $2303

Thus, Simple Interest = $2303

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 × 2303}/_{4700 × 7}

= ²³⁰³⁰⁰/₃₂₉₀₀

= 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) = $4700

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

Simple Interest = $2303 (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 $4700

= ⁷/₁₀₀ × 4700

= ^{7 × 4700}/₁₀₀

= ³²⁹⁰⁰/₁₀₀ = 329

Thus, simple Interest for 1 year = $329

Now,

∵ If the simple Interest is $329, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₃₂₉ years

∴ If the simple Interest is $2303, then the time = ¹/₃₂₉ × 2303 years

= ^{1 × 2303}/₃₂₉ years

= ²³⁰³/₃₂₉ = 7 years

Thus, time (T) = 7 years Answer

Similar Questions

(1) Find the amount to be paid if James borrowed a sum of $5000 at 4% simple interest for 8 years.

(2) Sarah took a loan of $5700 at the rate of 7% simple interest per annum. If he paid an amount of $8094 to clear the loan, then find the time period of the loan.

(3) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 4% simple interest for 8 years.

(4) How much loan did Elizabeth borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6540 to clear it?

(5) How much loan did Andrew borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7820 to clear it?

(6) Anthony had to pay $4687 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(7) Richard took a loan of $5200 at the rate of 10% simple interest per annum. If he paid an amount of $8840 to clear the loan, then find the time period of the loan.

(8) How much loan did Jason borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9240 to clear it?

(9) If Joseph borrowed $3700 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.

(10) What amount does David have to pay after 5 years if he takes a loan of $3400 at 9% simple interest?