Monica has decided that she wants to build enough retirement wealth that, if inv

Question

Monica has decided that she wants to build enough retirement wealth that, if invested at 10 percent per year, will provide her with $3,700 of monthly income for 25 years. To date, she has saved nothing, but she still has 30 years until she retires.

How much money does she need to contribute per month to reach her goal?

Monica has decided that she wants to build enough retirement wealth that, if invested at 10 percent per year, will provide her with $3,700 of monthly income for 25 years. To date, she has saved nothing, but she still has 30 years until she retires.

Explanation / Answer

in the problem ,

the future value of savings of 30 years should provide for the monthly income after retierment

In other words, future value of savings should be equal to the present value at year 30 of the monthly income recieved after retierment

PV of monthly income at year 30

= C * [1 - (1+i)^-n]/i

where i = interest rate per period = 10%/12

C= monthly income = 3700

n = number of periods = 25 * 12 = 300

PV = 3700 * [1 - (1+10%/12)^-300]/(10% /12)

= 407174.7512

the above value should be equal to Fv of savings

let x be the amount of monthly saving

FV = x * [(1+i)^n -1]/i

n = 30 * 12 = 360

FV = x * [(1+10%/12)^n -1]/10%/12 = 407174.7512

x = 180.13

hence she needs to save $ 180.13 per month

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