Question

Annuity payments. The Federal Reserve Bank of St. Louis has files listing historical interest rates on its website www.stlouisfeld.org. Find the link for “FRED” (Federal Reserve Economic Data). You will find a listing for the Bank Prime Loan Rate. The file lists the monthly prime rates since January 1949 (1949.01). What is the most recent prime rate? What is the highest prime rate over this period? If you buy a house for $150,000 at the current prime rate on a 30-year mortgage with monthly payments, how much are your payments? If you had purchased the house at the same price when the prime rate was at its highest, what would your monthly payments have been?

Answer 1

Maximum rate was 21.5% during 1980s

Monthly payment at that rate is:

Monthly payment	=	[P × R × (1+R)^N ] / [(1+R)^N -1]
Using the formula:
Loan amount	P	$                                                          150,000
Rate of interest per period:
Annual rate of interest		21.500%
Frequency of payment	=	Once in 1 month period
Numer of payments in a year	=	12/1 =	12
Rate of interest per period	R	0.215 /12 =	1.7917%
Total number of payments:
Frequency of payment	=	Once in 1 month period
Number of years of loan repayment	=	30
Total number of payments	N	30 × 12 =	360
Period payment using the formula	=	[ 150000 × 0.01792 × (1+0.01792)^360] / [(1+0.01792 ^360 -1]
Monthly payment	=	$                                                         2,692.00

Most recent rate is 3.25%

Payment is:

Monthly payment	=	[P × R × (1+R)^N ] / [(1+R)^N -1]
Using the formula:
Loan amount	P	$                                                          150,000
Rate of interest per period:
Annual rate of interest		3.250%
Frequency of payment	=	Once in 1 month period
Numer of payments in a year	=	12/1 =	12
Rate of interest per period	R	0.0325 /12 =	0.2708%
Total number of payments:
Frequency of payment	=	Once in 1 month period
Number of years of loan repayment	=	30
Total number of payments	N	30 × 12 =	360
Period payment using the formula	=	[ 150000 × 0.00271 × (1+0.00271)^360] / [(1+0.00271 ^360 -1]
Monthly payment	=	$                                                            652.81

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