Math Problems with Solutions

Solve the following problems completely. Show your work.
1. Mike has an annual expense of $846 for life insurance, a semi-annual car insurance
premium of $750,
and monthly charges of $90 for health insurance. Prorate the given expenses to find the
monthly cost.
Annual life insurance expense $ 846
This gives ¿ 846
12 =$ 70.5
Semi-annual car insurance expense $ 750
Gives 750
6 =$ 125
Monthly health insurance charges $ 90
The total monthly cost
¿ $ 70.5+$ 125+ $ 90=$ 285.5
2. Suppose that you invest $500 in an account that earns interest at an APR of 2.75%,
compounded
quarterly. Determine the accumulated balance after 5 years.
Accumulated balance= p ( 1+ i
n )
nt
Where p is the invested amount, r the APR and n the compounding times per year
¿ 500∗(1+ 0.0275
4 )4∗5
=$ 573.43
3. Your savings account pays an APR of 5.2%, compounded annually. If you deposit $600
at the end of
each year for 8 years, what will be the accumulated balance in the account?
Since the $ 600 is payable at the end of every year the payment steam is treated as an
ordinary annuity.

To calculate the accumulated values, we use the formula
FV =C∗( ( 1+ i ) n−1)/i ¿
Where c is the periodic cashflow, I the APR and n the number of payments
FV =600∗( (1+ 0.052 )8−1)/0.052
¿ $ 5770.61
4. Calculate the monthly payments for a home mortgage of $189,000 with a fixed APR of
5.875% for 15
years.
The future value is $ 189,000 and the interest rate is 0.05875 with a payment period of 15
years
Using the formula
FV =C∗( ( 1+ i ) n−1)/i ¿
We find that
FV /¿( ( 1+i ) n−1)/i¿=C
Hence
C= 189000
( 1+0.05875 )15−1
0.05875
=$ 8,197.59
5. Find the net monthly cash flow. (1 month = 4 weeks)
Income Expenses
Job $800 per week Rent $650 per month

Loan $3000 per semester Groceries $60 per week
Tuition and fees $2500 per semester
Miscellaneous $150 per week
Cash inflow
Job: 800∗4=$ 3200
Loan: 3000
3 =$ 1000
Total $ 4200
Cash outflow
Rent; $ 650
Grocery: 60∗4=240
Tuition: 2500
3 =$ 833.33
Miscellaneous; 150∗4=$ 600
Total; $ 2323.33
Net monthly cashflow is; 4200−2323.33=$ 1876.67
6. Prorate the following expenses and find the corresponding monthly expense. Lan pays a
semiannual premium of $450 for automobile insurance, a monthly premium of $120 for
health insurance, and an annual premium of $500 for life insurance. Round to the nearest
cent as needed.
Semiannual premium $ 450