When should saving start?

Quantitative Finance Level 2

Plan 1: Cora begins a retirement account at age 20. She starts with $2000 and then saves $2000 per year at 7% interest compounded annually for 10 years. Then she stops contributing to the account but keeps her savings invested at the same rate.

Plan 2: Mawiyah doesn't save any money in her twenties. When she turns 30 she starts with $2000 and then saves $2000 per year at 7% interest compounded annually for 35 years.

Which one has more at age 65?

Image Credit: Flickr Tax Credits .
Cora Mawiyah Cannot be computed Equal saving

Leonardo Arcenal Jr by Leonardo Arcenal Jr , 27, Philippines

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

2 solutions

At the end of the 10 years, the first one has 2000 x (1.07^10 + 1.07^9 + 1.07^8 + ... + 1.07^2 + 1.07) = 29567.20

This then is multiplied by 1.07^35 = 10.68 to yield 315,676.62

The other one gets 2000 x (1.07 + 1.07^2 + 1.07^3 + ... + 1.07^35) = 2000 x 137.4 = 274,800

Mawiyah doesn't catch up.

1 Helpful 0 Interesting 0 Brilliant 0 Confused

My result differs in that I do 2000 x (1.07 ^ 10 + 1.07 ^ 9 + 1.07 ^ 8 + ... + 1.07 ^ 2 + 1.07 ^ 1 + 1.07 ^ 0) and 2000 x (1.07 ^ 35 + 1.07 ^ 34 + 1.07 ^ 33 + ... + 1.07 ^ 2 + 1.07 ^ 1 + 1.07 ^ 0) respectively.

Cora and Mawiyah do invest 2000 more dollars in their tenth and thirty-fifth years of investing, respectively.

Sadie Robinson - 6 years, 11 months ago

i have the almost exact figures but in the other direction.

michael bye - 5 years, 9 months ago
Jerry Hill
Jan 17, 2016

At the end of 10 years. Cora has $27632.89. At the age of 65, Cora has $295024.865. At 65, Mawiyah has $276473.75.

0 Helpful 0 Interesting 0 Brilliant 0 Confused

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...