Question

Determine the value at the end of five years of a $6,000 investment (today) in a bank certificate of deposit (CD) that pays a nominal annual interest rate of 10 percent, compounded under either of the following three terms. Round your answers to the nearest cent.

1. Semiannually
   $  

2. Quarterly
   $  

3. Monthly
   $  

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

(a) When interest is compounded semi annually,

PV = Present value = $6000, r = 10%. Semi annual rate = 10 / 2 = 5%, and n = 5 * 2 = 10 semi annual years

Putting theses values in the above formula, we get,

FV = $6000 * (1 + 5%)¹⁰

FV = $6000 * (1 + 0.05)¹⁰

FV = $6000 * (1.05)¹⁰

FV = $6000 * 1.62889462678

FV = $9773.37

(c) When interest is compounded quarterly,

PV = Present value = $6000, r = 10%. Quarterly rate = 10 / 4 = 2.5%, and n = 5 * 4 = 20 quarter years

Putting theses values in the above formula, we get,

FV = $6000 * (1 + 2.5%)²⁰

FV = $6000 * (1 + 0.025)²⁰

FV = $6000 * (1.025)²⁰

FV = $6000 * 1.63861644029

FV = $9831.70

(c) When interest is compounded monthly,

PV = Present value = $6000, r = 10%. monthly rate = 10 / 12 = 0.833%, and n = 5 * 12 = 60 monthly years

Putting theses values in the above formula, we get,

FV = $6000 * (1 + 0.833%)⁶⁰

FV = $6000 * (1 + 0.00833)⁶⁰

FV = $6000 * (1.008333)⁶⁰

FV = $6000 * 1.64530860

FV = $9871.85