You decide to take out an ordinary interest loan of 30000 at

You decide to take out an ordinary interest loan of $30,000 at 4% on a 90 day note. In 45 days you decide to make a payment of $10,000 on due loan. What is your new principal? Explain how you got the answer. How much did you pay at the end of the loan overall? How does this differ from how much you would have paid overall had you not made a payment of $10,00 after 45 days?

Solution

a)

given

p₀ = $30,000

rate = 4% = 0.04

time = 45 days

payment made p = $10,000

let us find the interest of p₀

I = p₀*r*t = 30,000*(0.04/360)*45 = $150 = interest

now

p-I = $10,000 - $150 = $9,850 (amount. of partial payment left to reduce the principal)

Adjusted principal balance = $30,000- $9,850 = $20,150 = new principle

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b)

this part is not clear in the image please check it once by repposting it

here our new principle is $20,150 as $10,000 is already paid

so lets find out the interest

here we will take time = 45 days as 45 days is already finished

I = p*r*t = $20,150 (0.04/360)*45 = $100.75

so we will pay an amount of

$100.75 + $20,150 =  $20,250.75 over all at the end

so totally we paid $20,250.75 + $9,850 = $30,100.75

if no payment is done after 45 days then

p = $30,000

time = 90 days

I = p*r*t = $30,000(0.04/360)*90 = $300

so we will pay an amount of $300 + $30000 = $30,300

so there is a difference of $199.25