Question

Interest rates are 18% per annum compounded monthly in this entire problem.

a. Betty and Bob deposit $100 into a Sinking Fund at the end of each month for 20 years. Algebraically find the account value at the end of the 20 years. Your final answer should be correct to 3 places after the decimal point.

b. Bertha purchases a house for $200,000 with a 20 year mortgage of end of month payments. Algebraically find what the monthly payments are. Your final answer should be correct to 3 places after the decimal point.

Answer 1

a

FV of annuity	=	P * [ (1+r)^n -1 ]/ r
Periodic payment	P=	$                   100.00
rate of interest per period	r=
Rate of interest per year		18.0000%
Payment frequency		Once in 1 months
Number of payments in a year		12.00
rate of interest per period		0.18*1/12	1.5000%
Number of periods
Number of years		20
Number of payments in a year		12
Total number of periods	n=	240
FV of annuity	=	100* [ (1+0.015)^240 -1]/0.015
FV of annuity	=	230,885.44

Value of fund is $230,885.44

b

Monthly payment	=	[P × R × (1+R)^N ] / [(1+R)^N -1]
Using the formula:
Loan amount	P	$                                                          200,000
Rate of interest per period:
Annual rate of interest		18.000%
Frequency of payment	=	Once in 1 month period
Numer of payments in a year	=	12/1 =	12
Rate of interest per period	R	0.18 /12 =	1.5000%
Total number of payments:
Frequency of payment	=	Once in 1 month period
Number of years of loan repayment	=	20
Total number of payments	N	20 × 12 =	240
Period payment using the formula	=	[ 200000 × 0.015 × (1+0.015)^240] / [(1+0.015 ^240 -1]
Monthly payment	=	$                                                         3,086.62

Monthly payment is $3,086.62