company starting salary 75,000
retirement benefits 401k with annual contribution of 5% company will match 3% (for max contribution of 8% salary)
avg 401k return within mutual fund options at 8% per year
sign on bonus 0
annual bonus after 2 years of service annual bonus of $2000 per year ( 5% of annual bonus is deducted for retirement benefits)
house cost $100,000
mortgage rates 5% on 20 year mortgage
Calculate the following for 5 and 10 years
1. total income from salary
2. retirement account balances
3. annual bonus
4. total interest paid on mortgage
To calculate the total income from salary, retirement account balances, annual bonus, and total interest paid on mortgage for 5 and 10 years, let's break down the calculations step-by-step:
1. Total Income from Salary:
For both 5 and 10 years, the starting salary is $75,000.
- For 5 years: $75,000 × 5 = $375,000
- For 10 years: $75,000 × 10 = $750,000
2. Retirement Account Balances:
The annual contribution to the retirement account is 5% of the salary, and the company matches 3%, for a maximum contribution of 8%.
- For 5 years:
- Employee contribution: $75,000 × 0.05 × 5 = $18,750
- Company match: $75,000 × 0.03 × 5 = $11,250
- Total retirement contributions: $18,750 + $11,250 = $30,000
- Average annual return: 8% within mutual fund options
- Retirement account balance: $30,000 × (1 + 0.08)^5 = $43,105.81
- For 10 years:
- Employee contribution: $75,000 × 0.05 × 10 = $37,500
- Company match: $75,000 × 0.03 × 10 = $22,500
- Total retirement contributions: $37,500 + $22,500 = $60,000
- Average annual return: 8% within mutual fund options
- Retirement account balance: $60,000 × (1 + 0.08)^10 = $86,211.63
3. Annual Bonus:
After 2 years of service, there is an annual bonus of $2,000 per year, with 5% of the bonus deducted for retirement benefits.
- For 5 years:
- Bonus per year: $2,000 × 5 = $10,000
- Annual bonus for retirement: $10,000 × 0.05 = $500
- Total annual bonus received: $10,000 - $500 = $9,500
- For 10 years:
- Bonus per year: $2,000 × 10 = $20,000
- Annual bonus for retirement: $20,000 × 0.05 = $1,000
- Total annual bonus received: $20,000 - $1,000 = $19,000
4. Total Interest Paid on Mortgage:
The house cost is $100,000, and the mortgage rate is 5% on a 20-year mortgage.
- For 5 years:
- Monthly interest rate: 5% / 12 = 0.4167%
- Number of monthly payments: 20 years × 12 = 240
- Mortgage repayment amount: $100,000 × (0.004167 × (1 + 0.004167)^240) / ((1 + 0.004167)^240 - 1) = $639.58
- Total interest paid: ($639.58 × 240) - $100,000 = $53,499.20
- For 10 years:
- Monthly interest rate: 5% / 12 = 0.4167%
- Number of monthly payments: 20 years × 12 = 240
- Mortgage repayment amount: $100,000 × (0.004167 × (1 + 0.004167)^240) / ((1 + 0.004167)^240 - 1) = $639.58
- Total interest paid: ($639.58 × 480) - $100,000 = $106,998.40
Please note that these calculations do not include any raises, promotions, or changes in the housing market.
To calculate the various components for 5 and 10 years, let's break down each calculation step by step:
1. Total income from salary:
The starting salary is $75,000. Assuming there are no raises or promotions, the total income for both 5 and 10 years would simply be obtained by multiplying the starting salary by the number of years:
For 5 years: $75,000 * 5 = $375,000
For 10 years: $75,000 * 10 = $750,000
2. Retirement account balances:
The 401(k) annual contribution is 5% of the salary, while the company will match 3% of the salary for a maximum contribution of 8%. To calculate the retirement account balance, we need to consider both the individual's and the company's contributions, as well as the average 401(k) return at 8% per year.
For 5 years:
Individual Contribution: $75,000 * 0.05 * 5 = $18,750
Company Contribution: $75,000 * 0.03 * 5 = $11,250
Total Contributions: $18,750 + $11,250 = $30,000
To calculate the compounded return, we'll use the formula A = P(1 + r/n)^(nt), where:
A = balance after time t
P = initial principal (total contributions)
r = annual interest rate (8%)
n = number of times interest is compounded per period (annually)
t = number of periods (5 years)
Using this formula, the retirement account balance after 5 years would be:
Balance = $30,000 * (1 + 0.08/1)^(1*5) = $43,219 (rounded to the nearest dollar)
Following the same process, you can calculate the retirement account balance for 10 years.
3. Annual bonus:
After 2 years of service, there is an annual bonus of $2,000. However, 5% of this bonus is deducted for retirement benefits. Thus, the annual bonus net of retirement deductions is:
$2,000 - (0.05 * $2,000) = $1,900
For 5 years: $1,900 * 5 = $9,500
For 10 years: $1,900 * 10 = $19,000
4. Total interest paid on mortgage:
The mortgage rate is 5% on a 20-year mortgage, and the house cost is $100,000. To calculate the total interest paid, we'll use the formula A = P(1 + r/n)^(nt) - P, where:
A = total payment (principal + interest)
P = initial principal (house cost)
r = annual interest rate (5%)
n = number of times interest is compounded per period (annually)
t = number of periods (20 years)
For 5 years:
Principal = $100,000
Total Payment = $100,000 * (1 + 0.05/1)^(1*5) - $100,000 = $36,039 (rounded to the nearest dollar)
Total Interest Paid = Total Payment - Principal = $36,039 - $100,000 = -$63,961 (rounded to the nearest dollar; a negative value indicates a net savings on mortgage interest)
For 10 years:
Principal = $100,000
Total Payment = $100,000 * (1 + 0.05/1)^(1*10) - $100,000 = $72,703 (rounded to the nearest dollar)
Total Interest Paid = Total Payment - Principal = $72,703 - $100,000 = -$27,297 (rounded to the nearest dollar; a negative value also indicates a net savings on mortgage interest)
Note: A negative total interest paid means the interest saved is greater than the initial principal.