Aliza Ahora has decided to invest $1000 at the end of each year for the next...

Aliza Ahora has decided to invest $1000 at the end of each year for the next 10 years, after which she will allow it to compound at 8% for an additional 30 years. Manuel Mañana won’t save anything for 5 years, but will then invest $1000 annually for 35 years at 8%. What will the two portfolios look like in 40 years?

Expert Solution

Aliza Ahora

Future Value = Annuity * FVAF ( rate, number of years ) * FVIF ( rate, number of years )

= $ 1000 * FVAF ( 8%, 10 ) * FVIF ( 8%, 30 )

= 1000 * [ 1.08 + ...... + 1.08¹⁰] * [ 1.08³⁰ ]

= 1000 * 14.4866 * 10.0627

= $ 1,45,774.31 Answer

Manuel

Future Value = Annuity * [ FVAF ( rate, number of years ) - FVAF ( rate, number of years ) ]

= $ 1000 * [ FVAF ( 8%, 35 ) - FVAF ( 8%, 5 ) ]

= 1000 * [ 1 / 1.08 + ...... + 1 / 1.08⁴⁰] * [ 1 / 1.08 + ...... + 1 / 1.08⁵ ]

= 1000 * [ 259.0565 - 5.8667 ]

=1000 * 253.1898

= $ 253,189.80

jeff jeffy answered 2 years ago

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