Question

A college student takes out a $7500 loan from a bank. What will the balance of the loan be after one year(assuming the student has not made any payments yet)
a. if bank charges 3.8% interest each year ?
b. if the bank charger 5.3% interest each year ?

Answer 1

Answer:

(a) $7785

(b) $7897.5

Step-by-step explanation:

Given:

Loan = $7500

We need to find the balance of the loan be after one year(assuming the student has not made any payments yet).

The formula for amount or loan is

$A=P(1+r)^t$         .... (1)

where, P is principle, r is rate of interest and t is time in years.

(a) If bank charges 3.8% interest each year.

r = 3.8% = 0.038

Substitute P=7500, r=0.038 and t=1 in equation (1).

$A=7500(1+0.038)^1$

$A=7500(1.038)$

$A=7785$

Therefore, the balance of the loan be after one year is $7785.

(b) If the bank charger 5.3% interest each year.

r = 5.3% = 0.053

Substitute P=7500, r=0.053 and t=1 in equation (1).

$A=7500(1+0.053)^1$

$A=7500(1.053)$

$A=7897.5$

Therefore, the balance of the loan be after one year is $7897.5.

Answer 2

You can calculate the interest amount from the given rate of interest and then add it to initial loan amount to get the final payable amount.

The balance of the loan after one year for given interest rates will be

a) $7785

b) $7897.5

How to calculate the interest amount with a given rate and time?

There are mainly two types of interest. One which works only on principal(or say initial) amount, and one which works on amount + interest to be paid until now.

For 1 year case, if interest is applied annually, both interests are same since there is no interest before first year.

For 1 year, interest with R% rate for principal amount P is just R% of P which is $\dfrac{P}{100} \times R$

Evaluating all cases of interest rates applied on the principal amount of loan:

a) R = 3.8% each year

Since P = $7500, thus, interest for 1 year is 3.8% of $7500 which is

$I = \dfrac{7500}{100} \times 3.8 = 75 \times 3.8 = \ 285$

Thus, total payable amount = Principal amount + interest

Total amount = $7500 + $285 = $7785

b)  R = 5.3% each year

Since P = $7500, thus, interest for 1 year is 5.3% of $7500 which is

$I = \dfrac{7500}{100} \times 5.3 = 75 \times 5.3 = \ 397.5$

Thus, total payable amount = Principal amount + interest

Total amount = $7500 + $397.5 = $7897.5

Thus,

The balance of the loan after one year for given interest rates will be

a) $7785

b) $7897.5

Learn more about simple interest here:

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