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Find the periodic payments necessary to accumulate the amounts given in Exercises $7-12$ in a sinking fund. (Assume end-of-period deposits and compounding at the sa...

Question

Find the periodic payments necessary to accumulate the amounts given in Exercises $7-12$ in a sinking fund. (Assume end-of-period deposits and compounding at the same intervals as deposits.)$$ 20,000$ in a fund paying $3 %$ per year, with monthly payments for 10 years

Find the periodic payments necessary to accumulate the amounts given in Exercises $7-12$ in a sinking fund. (Assume end-of-period deposits and compounding at the same intervals as deposits.) $$ 20,000$ in a fund paying $3 %$ per year, with monthly payments for 10 years



Answers

Find the periodic payments that will amount to the given sums under the given conditions.
$S=\$ 80,000 ;$ interest is 6$\%$ compounded semiannually; payments are made at the end of each semiannual period for 9 years.

Suppose we want to end up with a final someone deposited in the account off $50,000 by making payments with 12% interest compounded quarterly for eight years. So we want to obey our dollars at the end of each quarter. We want to find the value of our the final Someone deposit. Also called the amount of a new team. Has the formula as equal are the amount off the payment times one plus i to the end Power minus one over I where n the notes, the number off interest periods and I represents the rate of interest there, period. Since we're making, um, payments compounded quarterly for eight years, the number off interest periods is an equal eight times four, which gives us 32 and, uh, the interest rate their beauty did I It's going to be 12 over 100 because we were being 12% interest and this will be divided by four. So we multiply with one over four simply by, so we get 0.3 rate of interest, period. Now, if we plug in as Sequel 50,000 and I and and we get so for our the amount for each of the payments. So, um, if we want to first right to the formula for arms we have we saw for our use is gonna be s divided by him. Want us? I do. And minus one over I or simply s I over one purse. I been minus one. And now we can replace us with 50,000. Multiply by 0.3 divided by one plus size 1.3 to the the exponents 32 minus one. Plugging this in tow, calculate and and rounding to decimal places, we will obtain 952 0.33.

Okay, so you want eight thousand dollars and our interest rate is four percent, but it's compounded monthly. So divided by twelve talk. Not the new year. And in the number of payments a payment periods. Well, it's five years, but monthlies twelve times. Five of sixty months in five years. And so the month payments will be eight thousand. Divine about this factor. One point here for over twelve, two, sixty, minus one, divided by one. Well, let's see. Stop it. I mean, so one plus your point zero for over twelve to the sixty months. One over zero point zero four. Over. There we go, and this gives us approximately one, one hundred twenty dollars and sixty seven cents.

Suppose we're making periodic payments off $1200 with a present interest compounded annually for nine years, We would like to find the present value of ordinary and unity for this we are gonna use the formula. Being equal are times one minus one. Plus I, the negative and divided by I where and is the number off consecutive interest periods. And I is the rate of interest per opinion. In this case, Since we have a percent interest compounded annually, I equals eight over 100 which is 0.8 and they, uh, 8% interest is compounded annually for nine years. The number off consecutive interests periods and is equal to nine are is 1200. So we have want minus one plus 0.8 is one points Europe eight two negative nine divided by this, you know, points. You know, using a calculator a rounding this to two decimal places. We get 7496 points $27

Okay, so we have that monthly payments are made of our annual payments. Our maid Sydney, one thousand two hundred eighty dollars. Interest rates your point zero seven compounded annually over nine years. And we want to know the present value or the value that, um, we need to invest now just once at the same interest rate, they gives us the same. Yeah. Final amount is just investing this one thousand two hundred eighty dollars every year at this interest rate. So we're looking for a pee. What we want to do is we want to take thousand two hundred eighty times this factor one minus one point seven to the minus nine over to your point here. Seven. And this gives us eight thousand three hundred and thirty nine give to sets.


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