a QMA question (1 Viewer)

[starkskyy]

Can someone show the working out to this question for me....for some reason im not getting it right.

Kate plans to retire at age 60. At that time, she wants to have enough to invest in a travel account so that she can go on a world trip every four years until she reaches 76, i.e. at ages 64, 68, 72 and 76. Each trip will cost $9,067. If the interest rate is 4.6% p.a. compounded quarterly, how much should she deposit in the travel account at age 60.

the answer is: 23,438.54

thanks

 

[leoyh]

Discount each trip that he plans to take at each 4 year interval to now i.e. when he is 60. So just PV em all and you will get the answer

 

[whoisurdaddy]

First off convert into an effective rate to make things a little easier.

(1+0.046/4)^4 - 1 = about 4.679%

Discount everything back to t=0

9057(1.0468)^-4 +9057(1.0468)^-8 +9057(1.0468)^-12 + 9057 (1.0468)^-16

Basically this means that storing $23,438.54 today into a bank earning an effective return of 4.679% will allow Kate to make 4 payments of $9057 throughout the course of 16 years.

 

[ascentyx]

First off convert into an effective rate to make things a little easier.

(1+0.046/4)^4 - 1 = about 4.679%

Discount everything back to t=0

9057(1.0468)^-4 +9057(1.0468)^-8 +9057(1.0468)^-12 + 9057 (1.0468)^-16

Basically this means that storing $23,438.54 today into a bank earning an effective return of 4.679% will allow Kate to make 4 payments of $9057 throughout the course of 16 years.

It's meant to be 9067 not 9057

Alternatively you can work in quarters rather than years.

4.6% p.a. compounded quarterly = 1.15% per quarter effective (dividing by 4).

PV = 9067 (v^-16 + v^-32 + v^-48 + v^-64) @ 1.15%
PV = 9,067[(1.15)^-16 + (1.15)^-32 + (1.15)^-48 + (1.15)^-64]

 

[whoisurdaddy]

yup was a typo sorry.