When I was considering what to do with my $10,000 Lottery winnings, my broker suggested I invest half of it in gold, the value of which was growing by 10% per year, and the other half in CDs, which were yielding 3% per year, compounded every 6 months. Assuming that these rates are sustained, how much will my investment be worth in 4 years? (Round your answer to the nearest cent.)
Yield = 5000(1.1)^4 + 5000(1.015)^8
= ....
Find the periodic payments necessary to accumulate $20,000 in a sinking fund paying 4% per year, with monthly payments for 5 years. (Assume end-of-period deposits and compounding at the same intervals as deposits. Round your answer to the nearest cent.)
To calculate the future value of your investments, we need to consider compounding. Let's break down the calculation for each investment:
1. Gold investment:
- Initial investment: $5,000
- Annual growth rate: 10%
- Number of years: 4
To calculate the future value of the gold investment, we can use the formula:
Future Value = Present Value * (1 + Growth Rate)^Number of Years
Future Value of Gold Investment = $5,000 * (1 + 0.10)^4
Calculating this, we find:
Future Value of Gold Investment = $5,000 * (1.1)^4 = $6,805.08
2. CD investment:
- Initial investment: $5,000
- Annual interest rate: 3%
- Compounded semi-annually (every 6 months)
- Number of years: 4
Since the interest is compounded semi-annually, we need to consider the compounding periods per year, which is twice (6 months).
To calculate the future value of the CD investment, we can use the formula:
Future Value = Present Value * (1 + (Interest Rate/Compounding Periods))^ (Compounding Periods * Number of Years)
Future Value of CD Investment = $5,000 * (1 + (0.03/2))^(2 * 4)
Calculating this, we find:
Future Value of CD Investment = $5,000 * (1 + 0.015)^8 = $5,622.95
Now, to determine the total future value of your investments, we sum up the future values of both investments:
Total Future Value = Future Value of Gold Investment + Future Value of CD Investment
Total Future Value = $6,805.08 + $5,622.95 = $12,428.03
Therefore, your investments will be worth approximately $12,428.03 in 4 years.