Answer:
The correct answer is a. $2275.28; b. 17.04 years
Step-by-step explanation:
Principal to be invested is $2000
Interest rate (r) per year is 6.5 quarterly.
Interest is calculated compoundly.
a. Time (t) for the investment is given to be 2 years.
Amount after two years is = Principal × [tex]( 1+ \frac{r}{100n}) ^ {nt}[/tex] where the value of n is 4.
⇒ A = 2000 × [tex]( 1+ \frac{6.5}{400}) ^ {8}[/tex]
⇒ A = $2275.28.
b. Now the value of A is given to be triple the principal = $ (3 × 2000).
Therefore we need to find the value of t.
⇒ 3 × 2000 = 2000 × [tex]( 1+ \frac{6.5}{400}) ^ {4t}[/tex]
⇒ ㏑ 3 = 4t × ㏑ ( 1.01625)
⇒ t = 17.04
Therefore it would take 17.04 years for the principal to triple.
