Question

Camila plans to go for vacation to Australia in 13 years from now. She estimates that she will need $19,178 for the trip. How much does she need to place in a saving account today that carns 6.37 percent per year (compounded quarterly) to accumulate this amount?

Answer 1

The formula of compound interest to calculate Future value from a given Present value, rate and time is as follows
F = P (1+r)^t
where, F = Future value
P = Present value
r = Rate of interest
t = Number of years
So, therefore we see that, P = F / [(1+r)^t]
Now, since it is compounded quarterly, therefore we will multiply time with 4 as well as divide rate by 4. This is because in case of time we will not take them as 13 years but (13X4) 52 quarters. Also in case of Rate we will not take them as 6.37% annual rate but (6.37/ 4) 1.59 rate per quarter.

Thus using the data given , we can find the Present value in the following way:
=> P = $19178 / [(1+ (6.37%/4))^13 years X 4]
=> P = $19178 / 2.274
=> P = 8433.6

Hence, Camila needs to place $8433.6 in a saving account today that earns 6.37 percent per year (compounded quarterly) to accumulate $19178 in 13 years from now.