Vince has $35,000 to purchase an annuity that will provide him with payments of $1,000 at the end of every three months. If the funds earn 8% compounded quarterly, how long will the payments continue?

A) 35 years
B) 36 years
C) 15 years
D) 9 years
E) 60 years

Question

Smeet Patel · Accepted Answer

Final Answer : C, Explanation :   To find the duration of the annuity, we use the formula for the present value of an ordinary annuity:   P = R × ( 1 − ( 1 + i ) − n ) i  P = \frac{R 	imes (1 - (1 + i)^{-n})}{i}  P = i R × ( 1 − ( 1 + i ) − n ) ​  , where   P  P  P   is the present value,   R  R  R   is the regular payment,   i  i  i   is the interest rate per period, and   n  n  n   is the number of periods. Here,   P = 35 , 000  P = 35,000  P = 35 , 000  ,   R = 1 , 000  R = 1,000  R = 1 , 000  , and   i = 0.08 / 4 = 0.02  i = 0.08/4 = 0.02  i = 0.08/4 = 0.02  . Solving for   n  n  n  , we find that the payments will continue for 60 periods, which is equivalent to 15 years (since payments are made quarterly).

Vince has $35,000 to purchase an annuity that will provide him with payments of $1,000 at the end of every three months. If the funds earn 8% compounded quarterly, how long will the payments continue?

A) 35 years
B) 36 years
C) 15 years
D) 9 years
E) 60 years

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Learning Objectives

Related questions

Vince has $35,000 to purchase an annuity that will provide him with payments of $1,000 at the end of every three months. If the funds earn 8% compounded quarterly, how long will the payments continue?A) 35 yearsB) 36 yearsC) 15 yearsD) 9 yearsE) 60 years

Definitions

Learning Objectives

Learning Objectives

Related questions

Vince has $35,000 to purchase an annuity that will provide him with payments of $1,000 at the end of every three months. If the funds earn 8% compounded quarterly, how long will the payments continue?

A) 35 years
B) 36 years
C) 15 years
D) 9 years
E) 60 years