Question

You want to save for a retirement party after you retire in 20 years. Your first party is free at year 20 and then you celebrate at the end of the year for the next 5 years. How much do you need to save each month for the next 20 years if each party costs $5,000. Your nominal annual interest rate is 8%, compounded semiannually.

Answer 1

The party will be held at the end of 21st to 25th year for a cost of $5000.
The interest rate is 8% and compounded semi-annually.
We will first calculate the effective annual interest rate
( 1 + ( 0.08 / 2 ) )² = 1.0816
( 1.0816 - 1 ) * 100 = 8.16%

Now we need to calculate the FV of the amount needed for the party
FV = PMT * ( 1+Interest Rate)^Duration
5000 * ( (1.0816)²¹ + (1.0816)²²+ (1.0816)²³ + (1.0816)²⁴+(1.0816)²⁵)
= $152806.67

The total amount needed is $152806.67
So we will proceed to calculate the monthly deposit required for the 20 years.
20 years = 240 months

=PMT(8.16%/12,240,,-152806.67)

= 254.31

The monthly deposit should be $254.31.