Time Value of Money (Nilai Uang dan Waktu), Present Value, Future Value, Anuitas

Summary

This video explores the Time Value of Money (TVM), a fundamental concept in finance and investment. It explains the relationship between the value of money over time and interest rates, covering key topics like Future Value (FV) and Present Value (PV). The script highlights how interest, when compounded annually or semi-annually, affects the growth of money. It also delves into Annuities, discussing how periodic payments accumulate over time and how to calculate both Future and Present Values of such cash flows. The video emphasizes the importance of compounding frequency and the formulas to apply for accurate calculations.

Takeaways

• 😀 Time Value of Money (TVM) is the concept that money has a different value at different times due to interest rates and the potential for investment or consumption.
• 😀 Future Value (FV) refers to how much a present amount of money will be worth in the future after accruing interest.
• 😀 To calculate Future Value, you can use the formula: FV = PV × (1 + r)^n, where PV is the present value, r is the interest rate, and n is the number of periods.
• 😀 Present Value (PV) is the reverse calculation, determining the current value of money that will be received in the future, based on the interest rate.
• 😀 To calculate Present Value, use the formula: PV = FV / (1 + r)^n, where FV is the future value.
• 😀 Compounding interest refers to how frequently interest is added to the principal, such as annually, semi-annually, or quarterly, affecting the future value.
• 😀 If interest is compounded semi-annually, the annual interest rate is divided by two and the number of periods is doubled in calculations.
• 😀 Quarterly compounding requires dividing the interest rate by four and multiplying the periods by four in the formulas.
• 😀 Annuities are regular, equal payments made over time. The Future Value of an Annuity can be calculated by adding up the future values of each individual payment.
• 😀 The Present Value of an Annuity is calculated by determining the total value of all future payments, discounted by the appropriate interest rate over the relevant periods.

Q & A

What is the time value of money (TVM)?

The time value of money (TVM) refers to the relationship between the value of money at different points in time and interest rates. It is a crucial concept in finance, investment, and accounting, stating that money today is worth more than the same amount in the future due to its potential earning ability.

What is the formula for calculating future value (FV)?

The formula for calculating future value (FV) is: FV = PV * (1 + r)^n, where PV is the present value, r is the interest rate, and n is the number of periods.

How do you calculate the future value of money if it is invested at 10% for two years, starting with $100?

To calculate the future value: After the first year, the value will be 100 * 1.10 = 110. After the second year, the value will be 110 * 1.10 = 121.

What is the present value (PV) of an amount that will be 110 after one year with a 10% interest rate?

The present value (PV) is calculated as PV = FV / (1 + r)^n. In this case, PV = 110 / 1.10 = 100.

What happens when interest is compounded more frequently than annually?

When interest is compounded more frequently than annually (e.g., semi-annually, quarterly, or monthly), the interest rate is divided by the number of compounding periods, and the number of periods is multiplied accordingly. This leads to a different future value calculation.

How do you calculate the future value of $1000 invested at 12% interest compounded semi-annually for one year?

For semi-annual compounding, the formula is FV = PV * (1 + r/2)^(2n). With $1000 at 12% interest for one year, FV = 1000 * (1 + 0.06)^2 = 1123.60.

What is the effect of compounding frequency on the future value of money?

The more frequently the interest is compounded, the higher the future value will be. This is because compounding interest means earning interest on previously earned interest, resulting in more accumulated value over time.

What is an annuity in the context of time value of money?

An annuity is a series of regular payments or investments made over time. The value of an annuity can be calculated using formulas for future value or present value, depending on whether you are looking to determine how much the annuity will be worth in the future or how much needs to be invested today.

How do you calculate the future value of an annuity where $100 is deposited each year for three years at an interest rate of 10%?

To calculate the future value of an annuity, you calculate the future value of each payment separately and sum them up. For $100 per year at 10% interest for three years: Year 1: 100 * 1.10^2 = 121; Year 2: 100 * 1.10^1 = 110; Year 3: 100 * 1.10^0 = 100; Total FV = 121 + 110 + 100 = 331.

What is the formula for calculating the present value of an annuity?

The formula for calculating the present value of an annuity is: PV = PMT * [(1 - (1 + r)^(-n)) / r], where PMT is the periodic payment, r is the interest rate, and n is the number of periods.