Question

A man invests $2000 in an account that pays 6.5% interest per year, compounded quarterly.

Answer 1

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 × $( 1+ \frac{r}{100n}) ^ {nt}$ where the value of n is 4.

⇒ A = 2000  × $( 1+ \frac{6.5}{400}) ^ {8}$

⇒ 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  × $( 1+ \frac{6.5}{400}) ^ {4t}$

⇒ ㏑ 3 = 4t × ㏑ ( 1.01625)

⇒ t = 17.04

Therefore it would take 17.04 years for the principal to triple.