You are given an annuity-immediate with 11 annual payments of 100 and a final balloon payment at the end of 12 years. At an annual effective interest rate of 3.5 percent, the present value at time 0 of all the payments is 1,000. Using an annual effective interest rate of 1 percent, calculate the present value at the beginning of the ninth year of all remaining payments.

The remaining amount is $360.34

Step-by-step explanation:

we will be using the present value annuity in this problem to solve for the present value of the ninth year of all remaining payments that means for the remaining 4 years including the ninth year, The present value formula :

the present value annuity calculates the present value of future payments that will be made through a period in a given time or given number of periods, so here we are given the following information:

$100 is a periodic payment so it will be represented by C.

1% is the interest rate (i) for the 12 years .

n is the period or the number of payments made so in this case we will use n=12 payments to calculate how much in present value is the amount by the end of the 12th payment year then we will subtract the present value for n=8 to calculate the present value at the end of the 8th year then the difference will be the present value at the beginning of the ninth year.

we will substitute the values on the above mentioned formula :

Present value = 100[(1-(1+1%)^-12)/1%] - 100[(1-(1+1%)^-8)/1%] compute

present value = $360.34 this will be the present value at the beginning of the 9nth year.

its 69.420

step-by-step explanation:

(a) common ratio in the given sequence is, 3

(b) push ups will do kendall do on the 20th week

step-by-step explanation:

geometric sequence is a sequence of numbers that follows a pattern were the next term is found by multiplying by a constant called the common ratio(r)

(a)

given the sequence: 6 , 18 , 54 , 162 ,

this sequence is geometric sequence where each term is 3 times the previous term.

therefore,

common ratio(r) = 3.

(b)

a formula for nth term of geometric sequence is given by;

,   where r is the common ratio between the successive terms and is the first term,

to find how many push ups will kendall do on the 20th week.

here. n = 20th term.

in the given sequence first term

then;

simplify:

therefore, push ups will do kendall do on the 20th week