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hiroshi and giulio share a common investment goal and once they reach their goals, they will withdraw their money. giulio starts out with 3 times as much money as hiroshi and it takes hiroshi 5 times longer than giulio to reach this goal. they both use the same bank that provides a 5% annual interest rate compounded quarterly. work out how long it takes hiroshi to reach his investment goal? give your answer correct to the nearest year.

Sagot :

If both of them choose the same bank, which offers a 5% annual interest rate compounded quarterly, Hiroshi will need 5.53 years to fulfill his investment target.

Let's suppose interest rate Giulio needs X years to accomplish his mission.

Hiroshi needs 5 times as long.

Hiroshi begins with an amount of A. Giulio's starting balance is 3A.

Both have the same goal amount.

So,

3A*((1+0.05/4)^(X*4) = A*((1+0.05/4)^(5X*4))

3*(1.0125^4X) = (1.0125^20X)

Taking the log from both sides

Log3 + log (1.0125 x 4X) = log (1.0125 x 20X)

20X*log3 + 4X*log(1.0125) + Log3 (1.0125)

X equals 1/16 * (log3/log(1.0125))

= 5.53 years

A percentage of the principal, or the amount loaned, is what a lender charges a borrower as interest. The annual percentage rate, or APR, is the usual unit used to express the interest rate on a loan (APR).

The interest rate amount earned from a savings account or certificate of deposit at a bank or credit union may also be subject to interest rates. Interest on these bank accounts is calculated as an annual percentage yield.

Learn more about interest rate here

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