Quiz 4 answer key
Math 1030-005 (Fall 2014)
AP R nY
) .
n
1. Compound interest formula: A = P × (1 +
(4 points)
Compute the balance of the following account: $20000 is invested for 20 years with an APR of
3.5% and quarterly compounding.
Ans: A = 20000 × (1 +
3.5% (4×20)
)
4
≈ 40152.61
2. Savings plan formula: A = P M T ×
R nY
(1+ AP
) −1
n
AP R
n
. (4 points)
You’d like to create a college fund for your child. Suppose you find a fund that offers an APR of
5%. How much should you deposit monthly to accumulate $70000 in 15 years?
Ans:
70000 = P M T ×
⇒P M T = 70000 ×
(1 +
(1 +
5% (12×15)
)
12
5%
12
5%
12
5% (12×15)
)
12
−1
−1
≈ 261.89
3. Continuous compounding formula: A = P × eAP R×Y .
(1) You put $7000 in account with an APR of 3% for 10 years. Assume the interest is calculated
using continuous compounding. What is the balance? (3 points)
(2) Calculate the annual return: ( PA )1/Y − 1. (1 point)
Ans: (1) 7000 × e3%×10 ≈ 9449.01.
(2) ( PA )1/Y − 1 = eAP R − 1 = e0.3 − 1 ≈ 0.3499 = 34.99%. (Wrong)
I have a topo here. The correct answer should be e0.03 − 1 ≈ 0.03045 = 30.45%
End of Quiz