Question

a) Complete the table to determine the balance A for P dollars invested at rate r for t years, compounded n times per year. (Round your answers to two decimal places.)

P = $3500, r = 3.5%, t = 20 years

n	A
1	$
2	$
4	$
12	$
365	$
Continuous compounding	$

B)Complete the table to determine the amount of money P that should be invested at rate r to produce a final balance of $120,000 in t years. (Round your answers to two decimal places.)

r = 3%, compounded continuously

t	P
1	$
10	$
20	$
30	$
40	$
50	$

c)

Find the effective rate of interest corresponding to a nominal rate of 8.5% per year compounded annually, semiannually, quarterly and monthly. (Round your answers to two decimal places.)

annually__ %

semiannually__ %

quarterly___%

monthly__ %

Answer 1

las P=$3500 8= 3-51. t = 20 years Here nal → A = ? na 2 > A= ? n=4 → A = ? n=12 -A ? n=365 → A-? nt Amount [X20 nel -> A- P(it) A = 3500 (1+ 0.025)*** 3500 (1+ (1+0.025 )2 470 3500 (1+0.005) $6964.26 $7005.59 2=2 A - 4X20 nou As $ 7026. 70 12x20 3 500 n=12 > A = $ 7040.95 (14 0.025 365 X20 n= 365 ) A = 3 500 it 0.035 365 $ 7047.89

b) A = $ 120,000 r=3% Compaunded Continuously ta! pa ? t-10 → P= ? t = 20 = P = ? t 30 < P-? E = eo > P = ? t= 50 p= ? (Compounded Continonly) Amount A = Pert 120,000 Pe 0.0341 => P= $116453.46 t=1 As 120,000 = e0.03 120,000 20.03x10 Pe9.03x19 t=10 120000 = be talle 20 > 120000 = Pee.03%20 0.03 X 30 P 0.03 x 30 t= 30 120,000 = -P= = $88898.18 as Pa $65857.39 - P: $ 48768.35 =) P= $ 36143.30 P= $26775.61 taho 120,000 = Pe0-03 xЧо t-50% 120,000 - Pe0.03450

c) The general formula for interest Veft (1+), given r = 8.5 = and for quarterly we compute 14 Wege = (1+0.985) Ñ 0.0877 which translates to interest rate of effective the rest of the approximates 8.777 To get below results consult the table case nominal rak (%) no of periods (n) eft rate (rest) vett = (1+ ongs ) .-= 0.085 nal T: 0-085 -8.51 n=2 r=0.085 b) rex = (1+0.055)? 12 0.087 8.68 n-4 c) r=0.085 reff = 0.087 = 8.7l. n = 12 ol) r= 0.05 Pet = (1+0.085)'>12 0.088 8.8 p