Homework 4 solutions
4.3
Assuming weekly compounding: r 6.89% ia
(1
0.0689 52 ) 1 0.07128 52
4.10 No. The debt debt interest rates are higher than than the return return on the investment investment funds. Pay down the highest-interest debt, which is the charge account debt. 4.20 (a) Quarterly interest rate = 1.5% 3 P P (1 0.015) N log 3 N log 1.015 N 73.7 73.78 8
quar quarte ters rs 73.78 / 4 = 18.5 years (b) Monthly interest rate = 0.5% 3 P P (1 0.005) N log 3 N log 1.005 220.27 months 220.27 / 12 = 18.42 years N
(c) 3 e0.06 N ln(3) 0.06 N N 18.31
years
4.24 (d)
Effective interest rate per payment period period i
= (1 + 0.01) 3 – 1 = 3.03%
0
1
2
3
4
5
6
$1,000
7
8
9
10
11
12
4.51 Given i 10%, N 10years, and A $95,000 365 $34,675,000
Daily payment with daily compounding: P $95,000( P / A,
10%
,3650) $219,170,331.48 365 Continuous payment and continuous compounding: P
10
0
Ae rt dt
e(0.10)(10) 1 $34,675,000 (0.10)(10) 0.1e $219,187,803.77
The difference between the two compounding schemes is only $17,472.27
4.58 Since payments occur annually, you may compute the effective annual interest rate for each year. 0.09 365 ) 1 9.416% , 365
0.09
i1
(1
F
$400( F / P , 9.416%, 2)(F / P , 9.417%, 2) $250(F / P , 9.416%,1)(F / P , 9.417%, 2
i2
e
1 9.417%
$100( F / P , 9.417%, 2) $100(F / P , 9.417%,1) $250
$1,379.93
4.61 (a) (i) $10,000( A / P ,0.75%,24) (b) (iii) B12
( / A,0.75%,12)
A P
4.74 Given Data: r = 7% compounded daily, N = 360 years
The effective annual interest rate is ia
(1 0.07 / 365) 365
1 7.25%
Total amount accumulated at the end of 25 years
9B;<888 ;E 9>< B;8 !
9>< B;8F! G "
9>
9>DC
4.78 $5, 025 $146.35( P / A, i, 48) i
1.46% per month
$146.35( P / A,1.46%, 33) 3, 810.91 4.80 Given: purchase price = $155,000, down payment = $25,000 P
Option 1:
i
7.5%/ 12 0.625% per month, N = 360 months
Option 2: For the assumed mortgage, P 1 $97,218 , i1
5.5%/ 12 0.458% per month , N 1 300 months , A1 $597 per month ;
For the 2nd mortgage P 2 N 2
$32,782 ,
i2
9%/12 0.75% per month ,
120 months
(a) For the second mortgage, the monthly payment will be !!
"! " ! # "$ #! $ $ ! %
&'!$()!" ! # "$*+(,-$.!*% &/.,+!(
$130, 000 $597( P / A ,i , 300) $415.27(P / A ,i ,120) i
r ia
0.5005% per month 0.5005% 12 6.006% per year 6.1741%
(b) Monthly payment
Option 1: A $130,000( A / P ,0.625%,360) $908.97
Option 2: $1,012.27 (= $597 + $415.27) for 120 months, then $597 for remaining 180 months.
(c) Total interest payment
Option 1: % &0*)+0( '1* &.'*$*** &.0($!!0+!* Option 2: I $228,932.4 $130,000 $98,932.4
(d) Equivalent interest rate: $908.97( P / A,i , 360) $597(P / A ,i , 300) $415.27(P / A ,i ,120) i
1.2016% per month
r 1.2016% 12 14.419% ia
15.4114%
per year