Question

Currently, I have $6,000 in my bank account that pays 5.2% APR with weekly compounding. In order to have $15,000 in this account in 4 years, how much money should I add to this account each month starting next month?

Answer 1

Given about an account,

Interest rate APR = 5.2% compounded weekly

We need monthly compounded rate as monthly deposits are made into the account. For this calculated effective annual rate

EAR = (1 + APR/n)^n - 1

Here n = 52 weeks in a year

=> EAR = (1 + 0.052/52)^52 - 1 = 5.3348%

So, monthly rate is calculated using formula

r = (((1 + EAR)^(1/n)) - 1) = (((1+0.053348)^(1/12)) - 1) = 0.4341%

Amount in account PV = $6000

amount needed in 4 years FV = $15000

Number of monthly period N = 4*12 = 48 months

Now using financial calculator to calculate monthly depsoit in the account. Use following values:

PV = 6000

FV = -15000

N = 48

I/Y = 0.4341

compute for PMT, we get PMt = $143

So, Monthly deposit in account is $143