Question

When Matt turned 25 he invested $2,500 in his retirement account for 10 years and stops. He earns an 8% return.

Clay invests $2,500 from age 36-65 (30 years) and stops. He earns the same 8% return.

How much money will each of then have at age 65? Who has more money and by how much?

Answer 1

MATT:

We will first find Future value at the end of 10 years of $2,500 deposited for 10 years

We will use future value of annuity formula as there is uniform series of cash flow for 10 years

FV = P [(1+R)^N-1]x (1+R) / R

WHERE,

• P=$2,500
• R=0.08
• N=10

FV = $2,500[(1.08)^10-1]*1.08 /0.08

=$39,113.72

Now, we he will invest $39,113.72 at 8% for 30 years from 36-65, there are no uniform cash flow only one time investment

=PV (1+r)^n

=$39,113.72 (1+0.08)^30

=$393,587.94

MATT will have $393,587.94 at the end of year 65

CLAY

We will use future value of annuity formula as there is uniform series of cash flow for 10 years

FV = P [(1+R)^N-1]x (1+R) / R

WHERE,

• P=$2,500
• R=0.08
• N=30

FV = $2,500 [((1+0.08)^30-1)x (1+0.08)] / 0.08

=$305,864.67

THUS, clay will have $305,684.67

Clearly, MATT will have more money.By ($393,587.94-$305,864.67) $87,723.27