Question

You put $8,000 in an account earning 5%. After 4 years you make another deposit into the same account. Three years later (that is, 7 years after your original deposit), the account balance is $20,000. What was the amount of the deposit at the end of year 4?

Answer 1

First we will calculate the value of account after 4 years as per below:

Here we will use the following formula:

FV = PV * (1 + r%)n

where, FV = Future value, PV = Present value = $8000, r = rate of interest = 5%, n= time period = 4

now, putting theses values in the above equation, we get,

FV = $8000 * (1 + 5%)4

FV = $8000 * (1 + 0.05)4

FV = $8000 * (1.05)4

FV = $8000 * 1.21550625

FV = $9724.05

So, value of the account after 4 years will be $9724.05.

Now, again we will use the above formula to calculate the deposit after 4 years, with changed values as per below:

FV = PV * (1 + r%)n

where, FV = Future value = $20000, PV = Present value , r = rate of interest = 5%, n= time period = 3

now, putting theses values in the above equation, we get,

$20000 = PV * (1 + 5%)3

$20000 = PV * (1 + 0.05)3

$20000 = PV * (1.05)3

$20000 = PV * 1.157625

PV = $20000 / 1.157625

PV = $17276.75

So, at the end of 4 years a total of $17276.75 was in the account. Out of this amount of $17276.75, amount already available in the account was $9724.05 (as calculated in first step). So, the amount of deposit at the end of year 4 was:

Amount of deposit at the end of year 4 = $17276.75 - $9724.05 = $7552.70