Question

If $19,000.00 is invested in an account for 30 years. Find the value of the investment at the end of 30 years if the interestis:(a) 7% simple interest:(b) 7% compounded monthly:

Answer 1

Hello there. To answer this question, we need to remember some properties in simple and coumpound interests investments.

For simple interest, the balance will be equal to P(1 + rt), in which P is the amount invested, r is the interest rate in years and t is the time (can be either years of months).

For compound interest, the balance will be equal to P(1 + r)^t.

So, using the values P = $19,000.00 and the time is equal to 30 years, we have for:

a) 7% simple interest

It means that r = 7% and then we can use the first formula

19000(1 + 0.07*30)

We converted the rate to decimals above

Multiplying the values, we have:

19000(1 + 2.1)

19000*3.1

$58.900

b) 7% compounded monthly

First, we need to convert the time from years to months, multiplying by 12

30*12 = 360 months

Using the second formula, we have:

19000(1 + 0.07)^(360)

Sum the values into parenthesis

19000*1.07^(360)