LOMA 308 Module 3 Study Guide with Complete Solutions

LOMA 308 Module 3 Study Guide with Complete Solutions Interest on investments, 3 factors affect their growth - Answer️️ -1. Interest rate 2. The type of interest 3. The time period during which the invested principal earns interest Interest rates - Answer️️ -Remember that interest is a fee that individuals and financial institutions pay (or charge) for the use of borrowed money. And the amount of interest earnings depends on the interest rate that's applied to the principal. Interest rates are usually stated in decimal form, so a 5 percent interest rate appears as 0.05 and a 2.5 percent rate appears as 0.025. Interest earned = $1,000 × 0.025 = $25 Calculating Interest Earned - Answer️️ -Principal (regular amount) × Interest rate = Interest earned Interest rate - Answer️️ -Interest rate = Interest amount ÷ Principal simple interest - Answer️️ -the amount of interest earned for one year is equal to the principal multiplied by the interest rate. As a result, when an investment earns simple interest, the nominal interest rate and the effective interest rate are the same. ©SOPHIABENNETT 2024/2025 7:35 PM The total amount of simple interest earned is equal to the interest for one year multiplied by the number of years in the investment period. At a constant annual rate of 5% simple interest, after 100 years the $10 account would have earned $50 in interest (100 x $0.50), and the total value of the investment would be $60.00. Compound interest - Answer️️ -When interest is compounded, the interest earned each investment period is added to the original principal amount, and that total is used as the beginning balance when calculating interest earnings for the next period. In this case, the effective interest rate is greater than the nominal interest rate. Compound Interest: At a constant annual rate of 5% compound interest, after 100 years the $10 investment would have earned $1,305.01 in interest and the total value of the investment would be $1,315.01. Effective Interest Rate - Answer️️ -The type of interest rate that includes the effects of compounding. The Rule of 72 - Answer️️ -Investors can use a simple rule of thumb known as the Rule of 72 to estimate how fast a principal sum doubles at a specified compound interest rate. The Rule of 72 states that, for a known interest rate, under annual compounding, the approximate number of years for a principal sum to double is 72 divided by the interest rate. ©SOPHIABENNETT 2024/2025 7:35 PM Years to double = 72 ÷ Interest rate Steadfast Insurance can calculate the interest amount it earned on an initial sum of money invested for one year at a specified interest rate by ( multiplying / dividing ) the principal by the interest rate. multiplying dividing - Answer️️ -Multiplying- An investor can calculate the interest amount earned on an initial sum of money invested for one year at a specified interest rate by multiplying the principal by the interest rate. Because ( simple / compound ) interest is applied to the same amount of principal each year, the amount of interest earned each year is the same, found by multiplying the principal amount by the interest rate. simple compound - Answer️️ -simple- Because simple interest is applied to the same amount of principal each year, the amount of interest earned each year is the same, found by multiplying the principal amount by the interest rate. Because the nominal interest rate includes the effects of compounding, it's usually greater than the effective interest rate. True False - Answer️️ -False- Because the effective interest rate includes the effects of compounding, it's usually greater than the nominal interest rate. And it increases even more if interest is compounded more than once each year. Steadfast Insurance can use the Rule of 72 to A. Estimate how fast a principal sum doubles at a specified compound interest rate ©SOPHIABENNETT 2024/2025 7:35 PM B. Determine the rate of interest a principal sum must earn to double in a certain number of years. Both A and B A only B only Neither A nor B - Answer️️ -The Rule of 72 states that, for a known interest rate, under annual compounding, the approximate number of years for a principal sum to double is 72 divided by the interest rate.The Rule of 72 can also help determine the rate of interest a principal sum must earn to double in a certain number of years. So far, you've seen how factors such as interest rates, types of interest, and time affect investment values. How do you think insurers use this information? (Choose all that apply.) - Answer️️ -The time value of money (TVOM) concept explains the effects of interest rates, types of interest, and time on investment values. Insurers use TVOM to determine the future value of an investment and the amount they need to invest today to earn a given amount in the future. TVOM doesn't help with investment choices. TVOM - Answer️️ -Insurers rely on the concept of the time value of money (TVOM) to explain the relationships among payment amounts, interest rates, and time.According to this concept, a sum of money has both a present value (PV) and a future value (FV). Present value - Answer️️ -In simple terms, the present value of an investment is the principal—the original amount invested before it's affected by interest. Present value = Principal Future value - Answer️️ -The future value is the invested principal plus the interest generated by the investment over time. ©SOPHIABENNETT 2024/2025 7:35 PM Future value = Principal + Interest earned The following statement(s) can correctly be made about present value and future value: A. Generally, a sum of money invested today has a present value that is less than its future value because of interest. B. A sum of money invested today for 10 years will grow to a larger sum than the same amount of money invested for 5 years. Both A and B A only B only Neither A nor B - Answer️️ -In the next part of the lesson, we'll take a closer look at future values. FV for single amount - Answer️️ -Analysts typically substitute present value (PV) for principal because, like principal, present value represents a sum of money before it is affected by interest. So, the formula for calculating the future value (FV) of a single amount for one period is FV = PV + Interest earned FV for one year investment - Answer️️ -For a one-year period, the amount of interest earned equals the present value multiplied by the interest rate, i. Because compounding only occurs when money is held for more than one period, we don't specify a value for the number of interest periods, n. We can express the formula for the interest earned on a one-year investment as follows: Interest earned = PV × i ©SOPHIABENNETT 2024/2025 7:35 PM Elegant Financial invested $300,000 for one year at 5 percent interest. How much did Elegant have at the end of the year? ___________ = PV × (1 + i ) $1,500,000 $450,000 $315,000 - Answer️️ -315,000 Fv of a single amount for mutiple periods - Answer️️ -The general formula for finding the future value of an investment earning compound interest, i, for n periods, can be written as: FV = PV × (1 + i )n So, if we deposited $100,000 into an account that earns 5 percent interest, compounded annually, for five years, the future value of this investment calculated using the formula would be: FV = $100,000 × (1.05)5 FV = $100,000 × (1.05)(1.05)(1.05)(1.05)(1.05) FV = $127,628 Montague Funds invested $100,000 at 3 percent interest compounded semi-annually. Montague wants to know what its investment will be worth in two years. When finding the future value of its investment, what value should Montague use for the number of periods and the interest rate? number of periods = 2, interest rate = 3 ©SOPHIABENNETT 2024/2025 7:35 PM number of periods = 2, interest rate = 1.5 number of periods = 4, interest rate = 1.5 number of periods = 4, interest rate = 3 - Answer️️ -nUMBER OF PERIODS = 4, INTEREST RATE = 1.5 - When interest is compounded more often than annually, you find the number of compounding periods by multiplying the number of years a sum is invested by the number of compounding periods in a year (2 years x 2 compounding periods per year = 4 periods). You then adjust the interest rate by dividing the stated interest rate by the number of compounding periods each year (3 ÷ 2 = 1.5). One true statement about a future value interest factor (FVIF) table is that: For any given period of time and any given interest rate, the FVIF is always greater than 1. For any given period of time, FVIF values increase as the interest rate decreases. For any given interest rate, FVIF values decrease as the investment period increases. To find the future value of a sum greater than $1 at a given rate of interest