Logarithmic Functions and Simple Interest
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1 Logarithmic Functions and Simple Interest Finite Math 10 February 2017 Finite Math Logarithmic Functions and Simple Interest 10 February / 9
2 Now You Try It! Section Logarithmic Functions Example Solve for x in the following equations: (a) 75 = 25e x (b) 42 = 7 2x+3 (c) 200 = (2x 1) 5 Finite Math Logarithmic Functions and Simple Interest 10 February / 9
3 Now You Try It! Section Logarithmic Functions Example Solve for x in the following equations: (a) 75 = 25e x (b) 42 = 7 2x+3 (c) 200 = (2x 1) 5 Solution (a) x (b) x (c) x Finite Math Logarithmic Functions and Simple Interest 10 February / 9
4 Applications Section Logarithmic Functions Recall that exponential growth/decay models are of the form A = ce rt. Using the natural logarithm, we can solve for the rate of growth/decay, r, and the time elapsed, t. Let s see this in an example. Finite Math Logarithmic Functions and Simple Interest 10 February / 9
5 Applications Section Logarithmic Functions Recall that exponential growth/decay models are of the form A = ce rt. Using the natural logarithm, we can solve for the rate of growth/decay, r, and the time elapsed, t. Let s see this in an example. Example The isotope carbon-14 has a half-life (the time it takes for the isotope to decay to half of its original mass) of 5730 years. (a) At what rate does carbon-14 decay? (b) How long would it take for 90% of a chunk of carbon-14 to decay? Finite Math Logarithmic Functions and Simple Interest 10 February / 9
6 Simple Interest Section Simple Interest Suppose you make a deposit or investment of P dollars or you take out a loan of P dollars. The amount P is called the principal. Finite Math Logarithmic Functions and Simple Interest 10 February / 9
7 Simple Interest Section Simple Interest Suppose you make a deposit or investment of P dollars or you take out a loan of P dollars. The amount P is called the principal. All of these things have an interest rate attached to them, essentially rent on the money, which is paid as interest. Finite Math Logarithmic Functions and Simple Interest 10 February / 9
8 Simple Interest Section Simple Interest Simple interest is computed as I = Prt Finite Math Logarithmic Functions and Simple Interest 10 February / 9
9 Simple Interest Section Simple Interest Simple interest is computed as where I = interest I = Prt Finite Math Logarithmic Functions and Simple Interest 10 February / 9
10 Simple Interest Section Simple Interest Simple interest is computed as where I = interest, P = principal I = Prt Finite Math Logarithmic Functions and Simple Interest 10 February / 9
11 Simple Interest Section Simple Interest Simple interest is computed as I = Prt where I = interest, P = principal, r = annual simple interest rate (written as a decimal) Finite Math Logarithmic Functions and Simple Interest 10 February / 9
12 Simple Interest Section Simple Interest Simple interest is computed as I = Prt where I = interest, P = principal, r = annual simple interest rate (written as a decimal), and t = time in years. Finite Math Logarithmic Functions and Simple Interest 10 February / 9
13 Section Simple Interest Example Example Suppose you deposit $2, 000 into a savings account with an annual simple interest rate of 6%. How much interest will accrue after 6 months? Finite Math Logarithmic Functions and Simple Interest 10 February / 9
14 Section Simple Interest Future Value Often, we might be more curious about how much will be in the account or how much will be owed on the loan after a certain period. This amount is called the future value. Another name for principal is present value. It is found by simply adding the original investment/loan amount to the interest accrued. Finite Math Logarithmic Functions and Simple Interest 10 February / 9
15 Section Simple Interest Future Value Often, we might be more curious about how much will be in the account or how much will be owed on the loan after a certain period. This amount is called the future value. Another name for principal is present value. It is found by simply adding the original investment/loan amount to the interest accrued. Definition (Future Value) A = P + I Finite Math Logarithmic Functions and Simple Interest 10 February / 9
16 Section Simple Interest Future Value Often, we might be more curious about how much will be in the account or how much will be owed on the loan after a certain period. This amount is called the future value. Another name for principal is present value. It is found by simply adding the original investment/loan amount to the interest accrued. Definition (Future Value) A = P + I = P + Prt Finite Math Logarithmic Functions and Simple Interest 10 February / 9
17 Section Simple Interest Future Value Often, we might be more curious about how much will be in the account or how much will be owed on the loan after a certain period. This amount is called the future value. Another name for principal is present value. It is found by simply adding the original investment/loan amount to the interest accrued. Definition (Future Value) and in a simplified form A = P + I = P + Prt Finite Math Logarithmic Functions and Simple Interest 10 February / 9
18 Section Simple Interest Future Value Often, we might be more curious about how much will be in the account or how much will be owed on the loan after a certain period. This amount is called the future value. Another name for principal is present value. It is found by simply adding the original investment/loan amount to the interest accrued. Definition (Future Value) A = P + I = P + Prt and in a simplified form A = P(1 + rt) Finite Math Logarithmic Functions and Simple Interest 10 February / 9
19 Section Simple Interest Future Value Often, we might be more curious about how much will be in the account or how much will be owed on the loan after a certain period. This amount is called the future value. Another name for principal is present value. It is found by simply adding the original investment/loan amount to the interest accrued. Definition (Future Value) A = P + I = P + Prt and in a simplified form where A = P(1 + rt) Finite Math Logarithmic Functions and Simple Interest 10 February / 9
20 Section Simple Interest Future Value Often, we might be more curious about how much will be in the account or how much will be owed on the loan after a certain period. This amount is called the future value. Another name for principal is present value. It is found by simply adding the original investment/loan amount to the interest accrued. Definition (Future Value) A = P + I = P + Prt and in a simplified form where A = future value, A = P(1 + rt) Finite Math Logarithmic Functions and Simple Interest 10 February / 9
21 Section Simple Interest Future Value Often, we might be more curious about how much will be in the account or how much will be owed on the loan after a certain period. This amount is called the future value. Another name for principal is present value. It is found by simply adding the original investment/loan amount to the interest accrued. Definition (Future Value) and in a simplified form A = P + I = P + Prt A = P(1 + rt) where A = future value, P =principal/present value, Finite Math Logarithmic Functions and Simple Interest 10 February / 9
22 Section Simple Interest Future Value Often, we might be more curious about how much will be in the account or how much will be owed on the loan after a certain period. This amount is called the future value. Another name for principal is present value. It is found by simply adding the original investment/loan amount to the interest accrued. Definition (Future Value) and in a simplified form A = P + I = P + Prt A = P(1 + rt) where A = future value, P =principal/present value, r =annual simple interest rate, Finite Math Logarithmic Functions and Simple Interest 10 February / 9
23 Section Simple Interest Future Value Often, we might be more curious about how much will be in the account or how much will be owed on the loan after a certain period. This amount is called the future value. Another name for principal is present value. It is found by simply adding the original investment/loan amount to the interest accrued. Definition (Future Value) and in a simplified form A = P + I = P + Prt A = P(1 + rt) where A = future value, P =principal/present value, r =annual simple interest rate, t =time in years. Finite Math Logarithmic Functions and Simple Interest 10 February / 9
24 Section Simple Interest Example Example Suppose you take out a $10, 000 loan at a simple annual interest rate of 3.2%. How much would be due on the loan after 10 months? Finite Math Logarithmic Functions and Simple Interest 10 February / 9
25 Now You Try It! Section Simple Interest Example You make an investment of $3, 000 at an annual rate of 4.5%. What will be the value of your investment after 30 days? (Assume there are 360 days in a year.) Finite Math Logarithmic Functions and Simple Interest 10 February / 9
26 Now You Try It! Section Simple Interest Example You make an investment of $3, 000 at an annual rate of 4.5%. What will be the value of your investment after 30 days? (Assume there are 360 days in a year.) Solution $3, Finite Math Logarithmic Functions and Simple Interest 10 February / 9
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