All answers should be rounded to 2 decimal places 1 A grandm

All answers should be rounded to 2 decimal places.

1. A grandmother wants to give her brand new grandson a gift of $25,000 on his 16th birthday. She finds an account that claims to average 9.45% interest compounded quarterly.

a) How much she deposit on the day of his birth in order to meet this goal if she decides to make only the one deposit? a) ___________________

b) How much interest will she earn on this single deposit? b) ___________________

c) How much should she deposit at the end of each quarter if she decides to make many deposits? c) ___________________

d) How much interest will she earn on these deposits? d) ___________________

Solution

1 a) Amount = Principal(1 +rate/4)^(n*t)

25,000 = P( 1+0.0945/4)^32

P = $ 11842.73 , she shoul deposit at the time of birth

b) Interest whe would earn = Amount - Principal = 25000 - 11842.73 = $13157.27

c) Use the formula for future value after a series of payments

F = x[(1+i)^n -1]/i

we have to find x

i = 0.045/4 = 0.023625

n = 16*4 = 64; F =25000

So, 25000 = x[1.02365^64 -1 ]/0.023625

=x*143.32

x = $174.43 amount she deposiyts at the end of each quarter

d) Interest = 25000 - 174.43*64 = $ 13836.48