Questions If You Invest 1500 In A Bank Account That Pays Sim
Questionsif You Invest 1500 In A Bank Account Which Pays Simple In
Questions: If you invest $1,500 in a bank account which pays simple interest at a rate of 3.5% per annum, for 18 months, how much interest will you receive when you withdraw the funds at the end of the term of investment? 2. If you invest $1,500 in an account that pays 5% per annum, simple interest, what will be the value of the account at the end of 40 months? You invested $2,500 into a term deposit account for 90 days, at the end of which there was $2,530 in the account. What simple rate of interest was paid on the account? If you invest $1,500 in a bank account, which pays 3.5% per annum interest, compounding annually, what will be the value of the account at the end of 18 months? If you invest $1,500 in a bank account, which pays 3.5% per annum interest, compounding monthly, what will be the value of the account at the end of 18 months? If you want to save $7,000 at the end of 5 years, in an account that pays 4% per annum, compounded annually. How much will you need to invest into the account at the beginning of the 5-year period? Interest is paid monthly at a monthly rate equal to 0.35%. What is the nominal rate per annum on the account? If you are offered a nominal amount equal to 8% per annum, compounding half yearly, what is the effective interest rate per annum? ABC Ltd issued a 3-year bond with a face value of $100, paying a half-yearly coupon of $2.50. However, no sooner had the bond been issued than interest rates on similarly rated debt rose to 8% per annum. What would be the value of the bond after the interest rate rise? ABC Ltd issued a 3-year bond with a face value of $100, paying a half-yearly coupon of $2.50. However, no sooner had the bond been issued than interest rates on similarly rated debt fell to 4% per annum. What would be the value of the bond after the interest rate fall?
Paper For Above instruction
Introduction
Investing in bank accounts and bonds involves understanding interest calculations, including simple interest, compound interest, and the impact of changing market interest rates. These financial concepts are essential for effective personal financial planning and investment decision-making. This paper explores various investment scenarios involving simple and compound interest calculations, the influence of interest rate changes on bond values, and the determination of interest rates from investment outcomes.
Simple Interest Calculations
Simple interest is computed based on the principal amount, the interest rate per annum, and the duration of the investment. It does not compound over time. The formula for simple interest is:
\[
I = P \times r \times t
\]
where \(I\) is the interest earned, \(P\) is the principal, \(r\) is the annual interest rate (in decimal), and \(t\) is the time in years.
For example, calculating the interest on a $1,500 investment at 3.5% for 18 months involves converting months into years (18 months = 1.5 years):
\[
I = 1500 \times 0.035 \times 1.5 = 78.75
\]
Thus, the interest received at the end of 18 months would be $78.75. The total amount after 18 months would be the principal plus interest, totaling $1,578.75.
Similarly, with a 5% simple interest rate over 40 months (which is approximately 3.33 years), the future value of $1,500 can be calculated as:
\[
FV = P + I = 1500 + (1500 \times 0.05 \times 3.33) \approx 1500 + 249.75 = 1749.75
\]
The interest rate earned over 90 days on a $2,500 deposit, resulting in a final balance of $2,530, can be determined as follows:
\[
I = 2530 - 2500 = 30
\]
\[
r_{monthly} = \frac{I}{P \times t} = \frac{30}{2500 \times (90/365)} \approx 0.0493 \quad \text{or} \quad 4.93\%
\]
This indicates a simple interest rate of approximately 4.93% over 90 days.
Compound Interest and Future Value
Compound interest involves earning interest on previously accumulated interest, leading to exponential growth of the investment. The general formula for compound interest is:
\[
FV = P \times (1 + \frac{r}{n})^{nt}
\]
where \(n\) is the number of compounding periods per year.
For an investment of $1,500 at 3.5% compounded annually over 18 months (1.5 years):
\[
FV = 1500 \times (1 + 0.035)^{1.5} \approx 1500 \times 1.0527 = 1579.05
\]
For monthly compounding:
\[
FV = 1500 \times (1 + \frac{0.035}{12})^{12 \times 1.5} \approx 1500 \times 1.05377 = 1580.66
\]
The difference illustrates how more frequent compounding yields slightly higher returns.
Determining Present Value for Future Savings
To save a target amount of $7,000 in 5 years at 4% annually, compounded annually, the initial investment can be calculated using the present value formula:
\[
PV = \frac{FV}{(1 + r)^t}
\]
\[
PV = \frac{7000}{(1 + 0.04)^5} \approx \frac{7000}{1.21665} \approx 5752.89
\]
Thus, an initial investment of approximately $5,752.89 is needed.
The monthly interest rate of 0.35% corresponds to a nominal annual interest rate obtained by multiplying by 12:
\[
Nominal\:rate = 0.35\% \times 12 = 4.2\%
\]
The effective annual rate (EAR) for this monthly rate is calculated as:
\[
EAR = (1 + 0.0035)^{12} - 1 \approx 0.0438 \quad \text{or} \quad 4.38\%
\]
This reflects the annualized yield accounting for monthly compounding.
Interest Rate Equivalence and Bond Valuation
When bond interest rates change, the bond's value adjusts inversely to reflect present value of future cash flows. The value of a bond is the sum of the present values of future coupon payments and the face value, discounted at the new market interest rate.
For a bond paying a semiannual coupon of $2.50 on a face value of $100, with remaining 3 years, and a market interest rate rising to 8% annually (4% semiannual), the present value is:
\[
PV = \sum_{t=1}^{6} \frac{2.50}{(1 + 0.04)^t} + \frac{100}{(1 + 0.04)^6}
\]
A higher market rate results in a lower bond value, reflecting the decreased attractiveness of the fixed coupon relative to new issues.
Conversely, if the interest rate falls to 4% annually (2% semiannual), the bond value increases:
\[
PV_{fall} = \sum_{t=1}^{6} \frac{2.50}{(1 + 0.02)^t} + \frac{100}{(1 + 0.02)^6}
\]
These calculations involve discounting each cash flow at the current market rate, illustrating the sensitivity of bond prices to interest rate fluctuations.
Conclusion
Understanding the mechanics of simple and compound interest, as well as bond valuation, enables investors to make informed decisions on savings, investments, and bond purchasing strategies. Changes in market interest rates significantly influence bond values, underscoring the importance of interest rate awareness. Effective financial planning requires applying these core principles to optimize investment outcomes and manage risk.
References
- Brigham, E. F., & Ehrhardt, M. C. (2016). Financial Management: Theory & Practice (15th ed.). Cengage Learning.
- Damodaran, A. (2012). Investment Valuation: Tools and Techniques for Determining the Value of Any Asset. Wiley Finance.
- Ross, S. A., Westerfield, R. W., & Jordan, B. D. (2019). Essentials of Corporate Finance (11th ed.). McGraw-Hill Education.
- Fabozzi, F. J. (2016). Bond Markets, Analysis and Strategies (9th ed.). Pearson.
- Investopedia. (2023). Simple Interest. https://www.investopedia.com/terms/s/simpleinterest.asp
- Investopedia. (2023). Compound Interest. https://www.investopedia.com/terms/c/compoundinterest.asp
- Choudhry, M. (2010). An Introduction to Bond Markets. John Wiley & Sons.
- Graham, B., & Dodd, D. L. (2008). Security Analysis: Sixth Edition. McGraw-Hill Education.
- Khan, M. Y., & Jain, P. K. (2008). Financial Management. McGraw-Hill India.
- Markowitz, H. (1952). Portfolio Selection. The Journal of Finance, 7(1), 77-91.