A person borrows $100,000 at a simple interest rate r = 24%. He is to repay...

A person borrows $100,000 at a simple interest rate r = 24%. He is to repay the loan with 2 payments, one at the end of 2 months and the other at the end of 6 months. The first payment is the same as the 2nd payment. Determine the size of the payments, using the end of 6 months as the focal date.

Expert Solution

The formula for simple interest final amount:

Amount (A) = P (1+rt)

Where:

A = Amount (principal + interest)
P = Principal Amount
r = Rate of Interest
t = Time Period in months or years

Given,

p = $100,000
r = 24% or 0.24
t = relevant time period
Let us say size of each payment is X.
It is also given in the problem that he has to repay the loan with two payments.
First one at the end of two months and the other at the end of six months.
The first payment is the same as the second payment.
By remembering the points mentioned above, we can make the following equation.

Therefore

100,000 [1 + (0.24)(6/12)] = X[1 + (0.24)(4/12)] + X
100,000 [1 + (0.24)(0.5)] = X(1 + 0.08) + X
100,000 (1.12) = X (1.08) + X
112,000 = 2.08 X
X = 112,000 / 2.08
X = $53,846.15

Finally, he has to pay $53,846.15 for each payment to cover both the interest and principal portion.

Thank you, please give an upvote

jeff jeffy answered 1 year ago

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