6. 11.42 points 0/6 Submissions Used My Notes New parents wish to save for their
ID: 3116943 • Letter: 6
Question
6. 11.42 points 0/6 Submissions Used My Notes New parents wish to save for their newborn's education and wish to have $42,000 at the end of 16 years. How much should the parents place at the end of each year into a savings account that earns an annual rate of 3% compounded annually? (Round your answers to two decimal places.) How much interest would they earn over the life of the account? Determine the value of the fund after 8 years. Submit Answer 7. 1.48 points 0N6 Submissions Used My Notes A corporation creates a sinking fund in order to have $680,000 to replace some machinery in 8 years. How much should be placed in this account at the end of each week if the annual interest rate is 6.9% compounded weekly? (Round your answers to the nearest cent.) How much interest would they earn over the life of the account? Determine the value of the fund after 2,4, and 6 years 2 years 4years 6 yearsExplanation / Answer
The formula to be used here is A = P[(1+r)n-1]/r, where A is the future value, P is the periodic payment, r is the rate per period and n is the number of periods.
6. Here, A = $42000, n =16, and r = 3% = 3/100 = 0.03. Then 42000= P[(1.03)16-1]/0.03 or, P = 42000*0.03/(1.604706439 -1)= 1260/0. 604706439 = $ 2083.66( on rounding off to the nearest cent). Thus the parents should save $ 2083.66 every year.
The interest earned over the life of the account is $ 42000-(16* $2083.66)= $ 8661.44
The value of the fund after 8 years is (2083.66/0.03)[(1.03)8-1]= 69455.33*0.266770081=$18528.60.
7. Here,A=$680000,n=8*52=416 and r = 6.9 % /52= 0.069/52 . Then 680000= P[(1+0.069/52)416-1]/ ( 0.069/52) or, P = (680000*0.069/52)(1.736087632-1) = (902.3076923)*(0. 736087632) = $ 664.18(on rounding off to the nearest cent). Thus, the amount to be placed in the sinking fund each week is $664.18.
The interest earned over the life of the account is $680000-( 416*$664.18)= $ 403701.12.
The value of the fund after 2 years is (664.18)[ [(1+0.069/52)104-1]/(0,069/52) = (664.18*52/0.069)* 0.147870542 = $ 74015.34.
The value of the fund after 4 years is (664.18)[ [(1+0.069/52)208-1]/(0,069/52) = (664.18*52/0.069)* = $ 158975.36.
The value of the fund after 6 years is (664.18)[ [(1+0.069/52)312 -1]/(0,069/52) = (664.18*52/0.069)* = $ 256498.47
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