A tale of Twins

$$Lucas and Lincoln are identical twins.

$$They have very different investment plans to provide for their retirement.

$$Study both plans and then decide who you think will have more money in his superannuation when they both reach $65$ years of age if their investment yield $5\%$ per annum compounded annually.

Lucas

I plan to put $$2000$ each year into my savings account beginning on my birthday when I turn $20$ years of age. When I turn $29,$ I will make my final contribution of $$2000$ Then I will leave the money invested in my savings account and let it grow, but I will make no further contributions.

Hint: How much will Lucas contribute to his super between ages $20$ and $30?$

Lincoln

I want to have some spending money while I$\text{'}$m young, so I will not open a savings accounting until I reach $30$ years of age. However, when I turn $30,$ I will put $$1500$ into a savings account each and every year until I turn $64.$ Then I will make my final contribution of $$1500.$

Hint How much will Lincoln contribute to his saving account between ages $30$ and $65?$

$$Both want to access superannuation

fund at $65.$

$$Investment rate $5\%$ p$.$a$.$

Who have more money?