Daniel must pay $10234 to the bank quarterly. He ha a debt with an interest rate of 10% compounded quarterly. How much did he borrow from the bank?

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Daniel must pay $10,234 to the bank quarterly. He has a debt with an interest rate of 10% compounded quarterly. How much did he borrow from the bank? So here we have this equation where payment equals rate times the present value over 1 -1 plus the rate raised to the negative end which stands for the number of periods. And I put a key over here on the left so that we know what each variable stands for. Our payment we know is $10,234. So we can substitute that in for p equals our rate. Well the rate is done a quarter since it's compounded quarterly, it's 10%. There's 4/4 in a year. 10% is a decimal is 0.1 over four Which gives me 0.025. So I get 0.025 times present value. That's what we're trying to solve for is how much did you borrow that present value over one minus one plus r. which is 0.025 to the negative end. Our end value is the number of periods. And since its quarterly our end value is four there's 4/4 in a year. So to the negative 4th this gives us 10,234 equals 0.25 times PV over one minus 1.025 raised to the -4. 10234 equals 0.025 times P. V. Over 1 -1.025 raised to the -4. And we get 0.9059 five, 10234 equals 0.025 times P. V. Over 1 -0.90595. I get 0.094049. I'm gonna multiply both sides by that denominator. 0.094049 0.09404. nine times. 10234 gives me 962.5011 equals 0.025 times TV. I'm going to divide both sides by 0.025. To isolate that PV 962.5011 divided by 0.025 Gives Me $38,500.04 for the present value. We're gonna round that to the nearest dollar. He probably didn't take out the four pennies. $38,500

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