Question

Bob and Kathy want to save a total of $500000 for retirement. How much should they deposit monthly into an account that pays 3.9% interest, compounded monthly, to meet there goal in 24 years

Answer 1

Answer:

The amount which Bob and Kathy deposited monthly is $16366.8

Step-by-step explanation:

Given as :

The amount that will be saved after retirement = A = $500000

The rate of interest applied = 3.9% compounded monthly

The time period = t = 24 years

Let The principal that should be deposited into account = $P

From Compound Interest

Amount = Principal × $(1+\dfrac{\textrm rate}{12\times 100})^{\textrm 12\times time}$

Or, $500000 = $P × $(1+\dfrac{\textrm r}{12\times 100})^{\textrm 12\times t}$

Or, $500000 = $P × $(1+\dfrac{\textrm 3.9}{12\times 100})^{\textrm 12\times 24}$

Or, $500000 = $P × $(1.00325)^{288}$

Or, $500000 = $P × 2.5458

∴ P = $\dfrac{500000}{2.5458}$

I.e P = $196401.91

So, The amount which they should deposit per month = $\dfrac{196401.91}{12}$ = $16366.8

Hence The amount which Bob and Kathy deposited monthly is $16366.8 Answer