Question

You have $7,500 to deposit. Regency Bank offers 15 percent per year compounded monthly (1.25 percent per month), while King Bank offers 15 percent but will only compound annually. How much will your investment be worth in 17 years at each Bank? (Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.)

Answer 1

Answer:

The investment will be worth $94,547 in the Regency Bank and $26,625 in the King Bank

Explanation:

Compound and Simple Interest

The main difference between simple and compound interest is the fact that in the simple interest, each amount earned by period of investment, is withdrawn from the account. This means that each new period of investment starts with the same principal P. The formula to compute the final value is

$FV=P(1+rt)$

Where r is the interest rate and t is the time.

In compound interest, each amount earned by period is added to the previous initial amount, making a new principal for the new period. This means that the account earns interest of interest. The formula is

$FV=P(1+r)^t$

Let's plug in the given values: P=7,500 ; r=15%=0.15 ; t=17 years. We must be careful to use the adequate values for r and t, because the investement is compounded monthly, thus we must convert both values to its equivalent monthly:

$i=0.15/12=0.0125$

$t=17*12=204$

$FV=7,500(1+0.0125)^{204}=\ 94,547.00$

Now for the simple interest:

$FV=7,500(1+0.15\cdot 17)= 26,625.00$