question 1:Hazel needs $7000 for her first year tuition at Lake head University

Question

question 1:Hazel needs $7000 for her first year tuition at Lake head University when she graduates in 2 years. She plans to make deposits into an account that earns 6.5% per year, compounded bi-weekly. How much should she deposit bi-weekly to meet her target amount.

question2: Edosa borrowed some money at 9.6%/a compounded monthly. Two years later, he paid $2000 toward the principal and the interest. After another, year, he paid another $2000. After another three years, he paid the remainder of the principal and the interest, which totaled $3000. How much money did he original borrow?

question 3: Bernard opens a savings account and invested $3196.88. How many years would Bernard need to keep his money in the savings account if the interest rate is 5.75%/a, compounded semi-annually, if he wants to make $5000?

question4: Filmon is putting his summer earnings into an annuity from which he can draw living expenses while he is at university. He will need to withdraw $900 per month for 8 months. Interest is earned at a rate of 6% compounded monthly. How much does Filmon need to invest at the beginning of the school year to finance the annuity.

Explanation / Answer

question 1:Hazel needs $7000 for her first year tuition at Lake head University when she graduates in 2 years. She plans to make deposits into an account that earns 6.5% per year, compounded bi-weekly. How much should she deposit bi-weekly to meet her target amount.

Real interest rate = ( 1+6.55 / 26)^26 - 1 = 6.7% ( No. of week in a year = 52 weeks)

7000 = amount*((1 + 6.7%/26)^26 - 1) / .002576

Amount = $260.662

question2: Edosa borrowed some money at 9.6%/a compounded monthly. Two years later, he paid $2000 toward the principal and the interest. After another, year, he paid another $2000. After another three years, he paid the remainder of the principal and the interest, which totaled $3000. How much money did he original borrow?

Real interest rate = (1+9.6%/12)^12 - 1 = 10.03%

PV of all payments = 2000/1.1003^2 + 2000 / 1.1003^3 + 3000 /1.1003^6

= $ 4844.04

question 3: Bernard opens a savings account and invested $3196.88. How many years would Bernard need to keep his money in the savings account if the interest rate is 5.75%/a, compounded semi-annually, if he wants to make $5000?

Real interest rate = (1+5.75%/2)^2 - 1 = 5.84%

5000 = 3196.88*1.0584^n

1.0584^n = 1.564

n = log1.564 / log1.0584 = 7.879 years

question4: Filmon is putting his summer earnings into an annuity from which he can draw living expenses while he is at university. He will need to withdraw $900 per month for 8 months. Interest is earned at a rate of 6% compounded monthly. How much does Filmon need to invest at the beginning of the school year to finance the annuity.

Real interest rate = (1+6%/12)^12 - 1 = 6.16%

Amount required = 900*(1 - 1/1.005133^8) / .005133 = $ 7036.496

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