MATH130 Calculus Interest Rates and Ordinary Annuity Problem Project this is a business calc class Math 130 Project Due: Thursday, May 9 This project may b

MATH130 Calculus Interest Rates and Ordinary Annuity Problem Project this is a business calc class Math 130 Project
Due: Thursday, May 9
This project may be done by yourself or with a group. The group may have a maximum
of 3 members. If done in a group, you only need to turn in one copy of the project for the
whole group. The project is to be done on a separate sheet of paper and written out
neatly showing your work carefully. You don’t need to re-write the whole question on
your paper but just the main points.
Part I:
Joe just graduated from College and has found a nice job. As a graduation gift his father
gave him $5000 as seed money for a down payment for a condominium that Joe plans to
purchase in three years. Joe wants to invest his $5000 into a savings account that gives
him the best rate.
Bank A has an interest rate of 6.02% compounded quarterly.
Bank B has an interest rate of 6% compounded monthly.
Which bank’s savings account should Joe go with so that he can earn the most money at
the end of the three years?
Hint: When Po is invested in a savings account for t years under the interest rate r (in
decimal form), and the interest is compounded n times each year, and then the end
balance is computed by
⎛
P = Po ⎜1 +
⎝
nt
r⎞
⎟ .
n⎠
Part II:
Since Joe plans to buy a condominium in three years, he needs to save more money for
the down payment. Joe goes to Bank B and wants to open another savings account where
he plans to deposit $400 every month. This account also pays 6% compounded monthly.
How much money will he have saved at the end of three years in this account?
Hint: This is an ordinary annuity problem. The future value, A, of an annuity is found
with the formula
nt
⎡⎛
⎤
r⎞
⎢ ⎜1 + ⎟ − 1⎥
n⎠
⎥.
A = m⎢ ⎝
⎢
⎥
r
⎢
⎥
n
⎣⎢
⎦⎥
Part III:
Joe is not happy with the amount he accumulates in part II. Help Joe find out how much
money he needs to put away each month so that he could accumulate $20,000 at the end
of three years. (This is not counting the money he gets in Part I.)
Part IV: Installment Payment
Jennifer wants to buy a $30,000 car. She has $5,000 to put as a down payment and needs
to borrow $25,000. Help Jennifer find out what her monthly payment will be if she plans
to pay monthly over a 5-year period at a 6% interest rate.
1. Divide the interest rate (in decimal form) by the number of payments per year.
Save the result for the next step and a future step.
2. Add 1 to the result of step 1.
3. Raise the result of step 2 to the power equal to the total number of payments to be
made (the product of the number of years and the number of payment per year.)
Save the result for the next step and for a future step.
4. Subtract 1 from the result of step 3.
5. Divide the result of step 3 by the result of step 4.
6. Multiply the result of step 5 by the amount of the original loan.
7. Multiply the result of step 6 by your result from step 1. The answer is the amount
of the installment payment.
Part V:
Let P denote the original amount of the loan, let r denote the annual interest rate, let n
denote the number of payments per year, and let t denote the number of years. Use the
seven steps just given to find an algebraic formula for computing the payment installment
amount m.

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