Question

Answer all these questions. Thank you!

1.

Problem 5.12 (Excel Video) Karen White is saving to buy a house in five years. She plans to put 20 percent down at that time, and she believes that she will need $29,000 for the down payment. If Karen can invest in a fund that pays 9.40 percent annual interest, compounded quarterly, how much will she have to invest today to have enough money for the down payment? (If you solve this problem with algebra round intermediate calculations to 6 decimal places, in all cases round your final answer to the nearest penny.) Excel Template (Note: This template includes the problem statement as it appears in your textbook. The problem assigned to you here may have different values. When using this template, copy the problem statement from this screen for easy reference to the values you've been given here, and be sure to update any values that may have been pre-entered in the template based on the textbook version of the problem.) Amount to be invested today

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Answer 1

1)Here FV = 29000$
R = rate of interest = 9.4%/4 = 2.35%
N = 5*4 =20
PV = FV/(1+r)^n
PV = 29000/(1+2.35%)^20
PV = 29000/(1.0235)^20
=29000/1.591318
= 18223.89$
Thus she need to invest $ 18223.89 today

2) Here PV = 190$
R = 7.7%
FV = 190*2 =380$
n = ?
FV =PV(1+r)^n
380 =190(1.077)^n
(1.077)^n =2
assuming n = 9
(1.077)^9 =1.9496
assuming n = 10
(1.077)^10 = 2.0996
using intrapolation we get
n = 9.336 years

N	Figure
9	1.9496
10	2.0996
1	0.15
	0.0504

=0.0504/0.15 = 0.336

3) table showing number of member at year 4

Year	Growth(in%)	Number of member
0		550
1	29%	710
2	29%	915
3	22%	1117
4	18%	1318
Thus number of member at end of 4 year is 1318

4)

Here FV = 4900$
A) R = 4.2%/365 = 0.0115%
n=3*365 =1095
PV = FV/(1+r)^n
=4900/(1.000115)^1095
=4900/1.134189
=4320.268$
B) R = 4.9%/12 = 0.4083%
N= 3*12 =36
PV = FV/(1+r)^n
=4900/(1.004083)^36
=4900/1.157993
=4231.457$
C) R = 5.2%/4 = 1.3%
n= 3*4 =12
PV = FV/(1+r)^n
=4900/(1.013)^12
=4900/1.167652
=4196.457$
D)R = 5.4%
n= 3
PV = FV/(1+r)^n
=4900/(1.054)^3
=4900/1.170905
=4184.796$

5) Here PV = 382000
FV = 476450
N = 4 years
FV = PV(1+r)^n
=476450=382000(1+r)^4
(1+r)^4 =1.24725
(1+r)^4*1/4 = 1.12475^1/4
(1+r) = 1.029826
r=0.029826
ie 2.9826%