A student invests $1000 in a bank account that pays an interest rate of 3.25% compounded monthly.

a) Develop a formula which will calculate the value of the investment (V) with respect to the number of compounding periods (n).

b) Hence, or otherwise, use the formula you developed in part a) to calculate:

• ? The value of the investment after 10 years
• ? The time taken for the investment to reach $10 000

 

Answer:

• a.)  V = PV(1+r/n)^nt 

• b.) 

V = $1383.42  

t = 70.945yrs

Step-by-step explanation

Formula needed for problems involving ANNUITY 

FV = PV(1+r/n)^nt 

Where:

FV - Final Value 

PV - Principal Value 

r - interest rate 

n - compounding period 

t - number of yrs 

• a.) 

V(investment) = FV 

PV = Investment 

Formula needed: 

FV = PV(1+r/n)^nt  

V = PV(1+r/n)^nt 

• b.) 

Given: 

PV or Investment = $1000 

FV = V = ? 

r = 3.25% 

n = 12 (compounded monthly) 

t = 10yrs 

V = PV(1 + r/n)^nt 

V = 1000(1 + 0.0325/12)¹²⁽¹⁰⁾ 

V = $1383.42 

Time t when V reaches $10000 

V = PV(1 + r/n)^nt  

10000 = 1000(1 + 0.0325/12)^12(t) 

Method 1: by using shift solve 

10000 = 1000(1 + 0.0325/12)^12(t)  

t = 70.945yrs

Method 2: by using logarithm 

10000 = 1000(1 + 0.0325/12)^12(t) 

10 = (1 + 0.0325/12)^12t 

log(10) = log[(1 + 0.0325/12)^12t]

og(10) = 12t log(1+0.0325/12) 

log(1+0.0325/12)log(10)?=12t 

t = 70.945yrs