Question

Suppose I deposit $1,800 in an account for which simple interest of 10% is payable. How much money will I have in the account at the end of 20 years? A. _______ How much would I have in the account if the interest compounded yearly instead? B._______. Question 9 options: A. $3,600 and B. $13,910 A. $5,400 and B. $13,910. A. $5,400 and B. $12,110 A. 3,600 and B. $12,110

Answer 1

A. $5,400 and B. $12,110

Step-by-step explanation:

As per given Data

Principal Value = $1,800

Interest Rate = 10% per year

Period = 20 years

A.

A Simple Interest is calculated by multiplying the interest rate to the principal value.

Interest Income = $1,800 x 10% = $180 per year

Interest Income = $180 x 20 years = $3,600

Total Account Balance after 20 years = $1,800 +$3,600 = $5,400

B.

Interest is compounded which means that the interest earned will be reinvested and next time interest income will also be earned on the the prior years interest income with the principal value. Interest Income for the period is added in the principal value for reinvestment.

Use following Compounding formula to calculate the account balance after 20 years.

Future value = Present value ( 1 + r )^n

Where

Present value = Principal = $1,800

r = Interest Rate = 10%

n = Numbers of years = 20 years

FV = $1,800 x ( 1 + 10% )^20

FV = $12,110

Answer 2

Accumulated sum

Simple interest $5400

Compound interest $12,109.4

Step-by-step explanation:

Simple interest

Under simple interest only the principal earns interest

The accumulated sum using simple Interest

Accumulated sum = P + (P× R × T)

Principal- 1,800, r- rate - 10%, n-period - 20

= $1,800 + (1800 × 10% × 20)

= $5400

Compound interest

Under compound interest is earning interest. The interest is calculated by multiplying the rate by the compound amount

Accumulated sum = P (1+r)^n

Principal- 1,800, r- rate - 10%, n-period - 20

= $1,800 ×(1.1)^(20)

= $12,109.4