Question

Problem 12. Show your work!

(a) Cersei wants to set up a college fund for her son Tommen. Investments deposited at the Iron Bank of Braavos earn 8% interest per year, compounded quarterly. If Cersei invests $7000 with the Iron Bank of Braavos, how long will it take her investment to be worth $126 000?

(b) Cersei also take out a $212 000 mortgage to buy a home in King’s Landing, amortizing it over 30 years at 5.5%, compounded monthly.

(a) What are her monthly payments?

(b) What is the remaining principal after 18 years?

Answer 1

First:

Payments to achieve future value	N=	Log(FV/PV)/ Log(1+r)
Future value	FV=	126,000
Present value	PV=	7,000
Interest rate:
Stated rate		8.0%
/ number of compounding periods per year		1
Interest rate per period	r=	8%
Periods to achieve future value	N=	Log( 126000/7000 )/ Log( 1+ 0.08 )
	N=	37.56

Second

a

Monthly payment	=	[P × R × (1+R)^N ] / [(1+R)^N -1]
Using the formula:
Loan amount	P	$                                                          212,000
Rate of interest per period:
Annual rate of interest		5.500%
Frequency of payment	=	Once in 1 month period
Numer of payments in a year	=	12/1 =	12
Rate of interest per period	R	0.055 /12 =	0.4583%
Total number of payments:
Frequency of payment	=	Once in 1 month period
Number of years of loan repayment	=	30.00
Total number of payments	N	30 × 12 =	360
Period payment using the formula	=	[ 212000 × 0.00458 × (1+0.00458)^360] / [(1+0.00458 ^360 -1]
Monthly payment	=	$                                                         1,203.71

b

Loan balance	=	PV * (1+r)^n - P[(1+r)^n-1]/r
Loan amount	PV =	212,000.00
Rate of interest	r=	0.4583%
nth payment	n=	216
Payment	P=	1,203.71
Loan balance	=	212000*(1+0.00458)^216 - 1203.71*[(1+0.00458)^216-1]/0.00458
Loan balance	=	126,683.64