# Finite Math

1.) Dan borrows $500 at 9% per annum simple interest for 1 year and 2 months. What is the interest charged, and what is the amount due?

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2.) A mutual fund pays 9% per annum compounded monthly. How much should I invest now so that 2 years from now I will have $100 in the account?

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3.) Hal deposited $100 a month in an account paying 9% per annum compounded monthly for 25 years. What is the largest amount he may withdraw monthly for 35 years?

Note:

For Question #3, the annuity continues to earn 9% monthly compounded interest for the 25 years of initial deposits and the 35 years of withdrawals. This is basically a 2-step problem.

1.) Find the total amount Hal has after depositing $100 per month in the annuity at 9% compounded monthly for 25 years.

2.) Use the amount from part 1 and find how much he can withdraw monthly for 35 years while it continues to earn 9% compounded monthly.

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4.) If an amount was borrowed 5 years ago at 6% compounded quarterly, and $6000 is owed now, what was the original amount borrowed?

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5.) $6000 is borrowed at 10% compounded semiannually. The amount is to be paid back in 5 years. If a sinking fund is established to repay the loan and interest in 5 years, and the fund earns 8% compounded quarterly, how much will have to be paid into the fund every 3 months?

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6.) How much principal is needed to get $800 in 2 years at 5% compounded monthly?

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7.) If Jack sold a stock for $35,281.50 that cost him $22,485.75 three years ago, what annual compound rate of return did Jack make on his investment?

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8.) The grand prize in an Illinois lottery is $6,000,000, which will be paid out in 20 equal annual payments of $300,000 each. Assume, the first payment of $300,000 is made, leaving the state with the obligation to pay out $5,700,000 in 19 yearly equal payments of $300,000 each. How much does the state need to deposit in an account paying 6% compounded annually to achieve this?

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9.) A mortgage of $125,000 is to be amoritized at 9% per annum for 25 years. What are the monthly payments? What is the equity after 10 years?

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10.) A couple wants to save for their child's college education. If they deposit $500 every 6 months at 6% compounded semiannually, how much will they have on hand at the end of 8 years?

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This solution is comprised of a detailed explanation to answer finance problems.