Question

You deposit $1000 for 4 years at an interest rate of 2.0%. If the interest is compounded annually, how much money do you have after the four years? A.$1,082.40 B. $1,100.00 C.$1,103.80 D.$1,344.90. Redo question 18 above with the same amount of deposit and the same interest rate, but with the interest compounded quarterly. How much money would you have at the end of the four years in this situation?

A.$1,081.70
B.$1,083.10
C.$1,110.80
D.$1,351.30

Answer 1

1000$(1,02^4) = 1082,43216$

Answer 2

First question : A. $ 1,082.40

Second question : B.$1,083.10

Explanation:

Since, the amount in the compound interest,

`A=P(1+(r)/(n))^(nt)`

Where, P is the principal amount,

t is the number of years,

n is the number of compound periods in a year,

r is the rate per period,

In first question,

P = $ 1000, t = 4 years, r = 2.0 % = 0.02 and n = 1

Hence, the amount of the money left after 4 years,

`A=1000(1+0.02)^4`

`=\$1082.43216`

Since, 1082.40 is nearer to 1082.43216.

Therefore, Option A is the correct option.

In second question,

P = $ 1000, t = 4 years, r = 2.0 % = 0.02 and n = 2

Hence, the amount of the money left after 4 years,

`A=1000(1+(0.02)/(4))^(16)`

`=\$ 1083.07115128\approx \$1083.10`

Therefore, Option B is the correct option.