Question

You borrow $10,000 from your parents at simple interest for 6 years at 7 %. Your parents put that on their mortgage, which has a rate of 7% compounded interest.How much does this end up costing your parents?

Answer 1

Money Borrowed(P) by me = $10,000

Time(n) = 6 years

Rate = 7% = 0.07 at Simple Interest

Formula of Amount under Simple Interest :

$A = P(1+nr)$

So, A = $10,000 (1 + (6*0.7))

= $10,000 (1 + 0.42)

= $10,000 * 1.42

= $14,200

If that money were rather put under 7% rate of compound interest

Then we know Amount under Compound interest :

$A = P(1+r)^{n}$

So, A = $10,000 * (1 + 0.07)⁶

= $10,000 * (1.07)⁶

= $10,000 * 1.50073

= $15,007.30

So, The cost to my parents is the loss they made by lending it to me rather than putting it under mortgage.

Loss = Amount under Compound Interest - Amount under Simple Interest

Loss = $15007.3 - $14200

= $807.3

So it ends up costing my parents $807.3

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