Principles of Economics

Calculations

The future value for one installment is given by FV=PV (1+r) ⁿ and FV= A*[(1+r) ⁿ -1]/r for continuous deposits. Where FV is the future value, PV is the principle value, r is the interest rate, and n is the number of contributions.

	20-32 years	32-65 years	Total
Beth	Contributions = $6000 FV=6,000*[(1.08) 12 -1]/(8/100)      = 6,000*18.9771      =113,862.76	Nil contributions FV with interest earning = 113,862.76(8/100)33  = 113,862.76*12.6760  =1,443,330	$1,443,330
Larry	Nil contributions	Contributions = $6000 FV= 6,000*[(1.08)33-1]/(8/100)   =6,000*145.9506     = 875,703.72	$875,703.72

Explanation

Beth earns more because of the Time Value of Money. That is, the value of money today is higher than the same amount tomorrow. Alternatively, the value of money today was lower than the same amount yesterday. Therefore, Beth’s money has a higher value than Larry’s since she began depositing twelve years before him. Besides, the compounding interest adds more value to Beth’s investment since the value compounded by the time Larry began investing was significantly higher. That is why Beth’s investment has a higher value, even though her contributions are almost a third of Larry.