MATH 1030-003, Quiz 4 Solution Spring 2012
MATH 1030-003, Quiz 4 Solution
Spring 2012
1. (4 pts) Find the annual percentage yield if a bank offers an APR of 5.5% compounded daily.
Let P = $1. Then we have,
0.055 365?1
A = $1 ? 1 + 365
= $1.05654.
So the relative change, or APY, becomes
AP Y = $1.05654 - $1 = 5.654%. $1
2. (4 pts) How much money will you have after 5 years if you deposit $1200 in an account with an annual interest rate of 2%, assuming that you earn simple interest?
A = P ? (1 + AP R ? Y ) = $1200 ? (1 + 0.02 ? 5) = $1320.
3. (4 pts) How much money will you have after 30 years if you deposit $5,000 today at an APR of 3.75% compouned monthly?
AP R n?Y A =P ? 1 + n
A =$5000 ?
1
+
0.0375 12
12?30
A =$15, 374.10
4. Suppose you have a home mortgage of $200,000 with an APR of 7.5% for 30 years. (a) (4 pts) Calculate the monthly payment.
PMT
=
P?
AP R n
1-
1
+
AP R n
-nY
PMT
=
$200, 000 ?
0.075 12
1-
1
+
0.075 12
-12?30
P M T = $1, 398.43.
(b) (Extra Credit: 2 pts) Determine the total amount paid over the term of the loan. T otal P aid = $1, 398.43 ? 12 ? 30 = $503, 434.
(c) (Extra Credit: 2 pts) Of the total amount paid, how much is paid toward the principal and how much is paid for interest? T oward P rincipal = $200, 000 or $200, 000 = 0.3973 = 39.73%, $503, 434 T oward Interest$503, 434 - $200, 000 = $303, 434 or 100% - 39.73% = 60.27%.
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