Question

Suppose Salma borrows $3500 at an interest rate of 9% compounded each year.

Assume that no payments are made on the loan.
Follow the instructions below. Do not do any rounding.
(a) Find the amount owed at the end of 1 year.
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(b) Find the amount owed at the end of 2 years.
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Answer 1

(a) The amount owed At the end of 1 year is $3,815

(b) The amount owed At the end of 2 years is $4,158.35

Explanation:

The given parameters on the loan amount are;

The amount Salma borrows = $3,500

The interest rate at which the loan is borrowed, r = 9% compound interest annually

The assumption are that no payments are made out of the loan

(a) The formula for finding a compound interest loan amount, 'A' is given as follows;

`A = P\cdot \left(1 + (r)/(n) \right)^(n\cdot t)`

Where;

A = The amount owed

P = The principal (the initial amount borrowed)

r = The interest rate = 9% = 0.09

n = The number of times the interest is paid per unit period, 't' = 1

t = The number of periods of the loan = Number of years

At the end of 1 year, t = 1, we get;

`A = 3,500 * \left(1 + (0.09)/(1) \right)^(1 * 1) = 3815`

The amount owed, A = $3,815 at the end of 1 year

(b) The amount owed at the end oy 2 years is found by plugging in t = 2 years into the formula for finding the amount owed by the borrower, therefore, we get;

`A = 3,500 * \left(1 + (0.09)/(1) \right)^(1 * 2) = 4,158.35`

At the end of 2 years, the amount owed, A = $4,158.35