Suppose You Divide Your Life into Two Periods: Working Age

question 99

Essay

Suppose you divide your life into two periods: working age and retirement age.When you work,you earn labor income Y; when retired,you earn no labor income,but must live off your savings and the interest it earns.You have no initial assets.You save the amount S while working,earning interest at rate r,so you have (1 + r)S to live on when retired.Because you don't need to consume as much when retired,you want to set consumption when working twice as high as consumption when retired.
(a)Suppose you earn $1 million over your working life,and the real interest rate for retirement saving is 50%.How much will you save,and how much will you consume in each part of your life?
(b)Suppose your current income went up to $2 million when working.Now what will you save and how much will you consume each period?
(c)Suppose a social security system will pay you 25% of your working income when you are retired.Now (with Y = $1 million as in part (a)how much will you save and how much will you consume each period?
(d)Suppose the interest rate rises.Will you save more or less?

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Definitions:

Scale

A system or series of marks used for measuring or quantifying objects, distances, or the relative level or intensity of something.

APR

Annual Percentage Rate; the annual rate charged for borrowing or earned through an investment, including any fees or additional costs associated with the transaction.

Mortgage

A loan used by individuals and businesses to purchase real estate without paying the entire purchase price upfront, wherein the property itself serves as collateral for the loan.

Interest

The cost of borrowing money, typically expressed as a percentage of the amount borrowed.