Question

Valeri invested $5000 at 9.25% compounded quarterly. After 18 months, the rate changed to 9.75% compounded semi-annually. What amount will Valeri have 3 years after the initial investment?

Answer 1

Here we will use the following formula:

FV = PV * (1 + r%)ⁿ

where, FV = Future value, PV = Present value, r = rate of interest, n= time period

First we will calculate the FV, future value for first 18 months by the above formula as per below:

PV = $5000, r = 9.25% compounded quarterly. So quarterly rate = 9.25% / 4 = 2.3125%, n = 1.5 * 4 = 6 quarters

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

FV = $5000 * (1 + 2.3125%)⁶

FV = $5000 * (1 + 0.023125)⁶

FV = $5000 * (1.023125)⁶

FV = $5000 * 1.14702314292

FV = $5735.11571461

The amount after 18 months is $5735.12

After 18 months, rate is changed, so we will calculate the FV, future value for next 18 months by the above formula as per changed rate with below figures:

PV = $5735.12, r = 9.75% compounded semi annually. So semi annual rate = 9.75% / 2 = 4.875%, n = 1.5 * 2 = 3 Semi annual years.

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

FV = $5735.12 * (1 + 4.875%)³

FV = $5735.12 * (1 + 0.04875)³

FV = $5735.12 * (1.04875)³

FV = $5735.12 * 1.15349554492

FV = $6615.4353

So, the amount after 3 years will be $6615.44.