Calculating Principal, rate, and Time

1. Philip wants to supplement his pension by $2000 per month with income from his investments. His investments pay him monthly and earn 6% p.a. What value of investments must Philip have in his portfolio to generate enough interest to give him his desired income?

1. What is the amount to which $7,250.00 will grow at 7.75% p.a. in 3 months?
2. Bunny's Antiques received $88.47 interest on a 120-day term deposit of $7800. At what rate of interest was the term deposit invested?

3.Anne's Dress Shop borrowed $3200 to buy material. The loan was paid off seven months later by a lump-sum payment that included $168 of interest. What was the simple rate of interest at which the money was borrowed?

4.A bank pays an interest of 4.5% for a three-month term deposit. Calculate the amount that Mark must invest to earn an interest of $100.00.

Future Value

1. Prairie Grains Cooperative wants to invest $45 000 in a short-term deposit. The bank offers 1.3% interest for a one-year term and 1.1% for a six-month term.
   1. How much would Prairie Grains receive if the $45 000 is invested for one year?
   2. How much would Prairie Grains receive at the end of one year if the $45 000 is invested for six months and then the principal and interest earned is reinvested for another six months?
   3. What would the one-year rate have to be to yield the same amount of interest as the investment described in part (b)?

Break Even and Contribution Rate, and Margin

1. Tara makes and sells scarves for children and adults. She is able to sell the scarves for $18 per unit. Materials for the scarves cost $4 each. She has fixed cost per month of $280, and estimates that she can make and sell 80 scarves each month. How many scarves does Tara need to sell to break even?

1. A manufacturer makes high-class pens. The pen case costs $7.26 each, the ink holder costs $1.26 each, the spring costs $.07 each and the gold pen case costs $0.91 each. The plant has general and administrative costs of $55000 and fixed selling expenses of $37500. The pens sell of $39.95 each. Plant capacity is 4000 pens per period. At what percentage of capacity is the break-even point?

2. A vehicle accessory shop is considering buying a new style of wheels for $168 and selling them at $369.60 for each wheel. Fixed cost related to this new style of wheel amounts to $2465. It is estimated that 16 wheels per month could be sold. How much profit will the accessory shop make each month?

3. Sanford and Sons, a local manufacturer of a product that sells for $13.50 per unit. Variable cost per unit is $7.85 and fixed cost per period is $1,220. Capacity per period is 1100 units.

Perform a break-even analysis showing an algebraic statement of:

1. The revenue function.
2. The cost function.
3. Calculate the break-even point in units.