Raymond puts the money he inherited in an investment that earns 4.4% per year, compound semi-annually. After 12 years his investment had grown to $35,402.06. Raymond then invested the $35,403.06 at 5% per year, compound quarterly for the next 5 years.
Is there a question?
Also, which is it, 35402.06 or 35403.06 ?
To find the future value of an investment, we need to use the formula for compound interest:
Future Value = Principal * (1 + (Interest Rate / Number of Compounding Periods))^(Number of Compounding Periods * Number of Years)
Let's solve the first part of the problem:
1. The initial amount Raymond invested is not given, but we know that after 12 years, it grew to $35,402.06 with an interest rate of 4.4% per year, compounded semi-annually.
Future Value = Principal * (1 + (0.044 / 2))^(2 * 12)
35,402.06 = Principal * (1 + 0.022)^24
Simplifying:
35,402.06 = Principal * 1.59084886668
Divide both sides by 1.59084886668:
Principal = 35,402.06 / 1.59084886668
Principal ≈ $22,276.02
Therefore, Raymond initially invested approximately $22,276.02.
Now, let's move on to the second part of the problem:
2. Raymond then invested the $35,402.06 at an interest rate of 5% per year, compounded quarterly for the next 5 years.
Future Value = Principal * (1 + (0.05 / 4))^(4 * 5)
Future Value = $35,402.06 * (1 + 0.0125)^20
Simplifying:
Future Value = $35,402.06 * 1.28008401404
Future Value ≈ $45,301.33
Therefore, after five years of compound quarterly interest, Raymond's investment grew to approximately $45,301.33.