Question

Kevin plans to retire in 30 years, and he plans to save up $250,000 for retirement. He has two options
• Plan 1: compounded monthly with an APR of 3.3%
• Plan 2: compounded quarterly with an APR of 3.5%
Compare these two options to see which one is more beneficial for Kevin. When you make the comparison,
you should at least calculate
1. the amount he needs to deposit each time period
2. the total interest accrued

Answer 1

The rate of growth of the amount invested with time in Plan 1 is slightly higher than the amount invested in Plan 2.

• The option most beneficial to Kevin by comparison is Plan 1

Reasons:

The number of years for the investment = 30 years

The amount he plans to save = $250,000

The investment plan options are;

Plan 1: Compounded monthly investment with APR, r = 3.5%

The formula for monthly contributions is presented as follows;

$\displaystyle FV = \mathbf{\frac{PMT \cdot \left( 1 + \frac{r}{n}\right)^{n\cdot t} - 1}{\frac{r}{n} }}$

Which gives;

$\displaystyle 250,000 = \mathbf{\frac{PMT \cdot \left( 1 + \frac{0.033}{12}\right)^{360} - 1}{\frac{0.033}{12} }}$

Solving gives;

• The amount he needs to deposit each month, PMT ≈ $256.18

The total deposit = 360 × $256.18 = $92,224.2

• Total interest accrued  = $250,000 - $92,224.2 ≈ $157,775.78

Plan 2: Compounded quarterly, with APR, r = 3.3

Which gives;

$\displaystyle 250,000 = \mathbf{\frac{PQT \cdot \left( 1 + \frac{0.035}{4}\right)^{120} - 1}{\frac{0.033}{4} }}$

• The amount he needs to deposit each quarter ≈ $769.34

The total deposit = $769.34 × 120 = $92,321.3336

• Total interest accrued = $250,000 - $92,321.3336 ≈ $157,678.67

The total interest accrued by investing in plan 1 which is approximately

$157,775.78 is larger than the interest accrued on Plan 2 which is

approximately $157,678.67

• The option most beneficial to Kevin is Plan 1, due to the higher total interest accrued

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