You decide to place $12,000 on deposit for 4 years. The bank offers you 6 percent compounded annually. a. What is the total amount of money in the account at the end of 4 years? (2.4) b. What value of simple interest would be necessary to have the same amount of money in the account at the end of 4 years?

a) The total amount of money in the account = $15, 149.72

b) Simple interest rate to have the same amount as (a) above = 6.56%

Explanation:

Interest rate is price paid by a borrower for the use of money and the return earned by a lender for postponing his consumption in favour of investment.

Future Value : This is total amount due in the future where a sum of money is invested at a particular rate today (simple or compound interest) for certain number of years.

Simple interest and compound interest

Interest can be computed in two different ways;

simple interest compound interest

Simple interest: This is the interest paid on the principal invested or borrowed. To calculate the future value under simple interest, we use he formula below:

FV = P + (P * R * T)

Compound interest : This is the interest earned on both the principal amount plus any already earned interest i. e the compound amount. Under the compound interest, not only will the principal amount earn interest but also the already earned interest.

The future value under compound interest is computed as follows:

FV = P * (1 + r) ^ (n)

P - principal deposit, rate per period, n - number of period

FV = 12,000 * (1+0.06) ^ (4)

= 15, 149.72

The total amount of money in the account = $15,149.72

FV = P + (P * R * T)

15,149.72 = 12,000 + (12000 * R * 4)

15,149.72 - 12,000 = 12,000 * R * 4

(15,149.72 - 12,000) = R * (4 * 12000)

(15,149.72 - 12000) / (4*12000) = R

0.0656 = R

6.56% = R

Simple interest rate to have the same amount as (a) above = 6.56%