MHB How Much Can a School Earn from a $50000 Donation Invested for 3 Years?

[kellyblaack]

An alumnus of a local high school donated $50000 to the school. The amount was invested for 3 years at 7.75%, compounded quarterly. The school has agreed to use only the interest earned on the investment to buy sports equipment. How much money will be available for sports equipment at the end of the investments term?

 

[tkhunny]

An alumnus of a local high school donated $50000 to the school. The amount was invested for 3 years at 7.75%, compounded quarterly. The school has agreed to use only the interest earned on the investment to buy sports equipment. How much money will be available for sports equipment at the end of the investments term?

It is very important to have basic accumulation formulas in your pocket. Memorize this one!

P\cdot \left(1 + \dfrac{i}{m}\right)^{n\cdot m} -- This gives the accumulated value.

P is the beginning principle balance.
i is the constant nominal annual interest rate.
m is the number of compounding periods in a single year.
n is the number of years to accumulate.
By extension, n * m is the number of compounding periods in the entire accumulation period.

Let's see if this leads you to answering the question. :-)

 

[HallsofIvy]

Three years has only 12 quarters so it is not that hard to do it "by hand".

For the first quarter, 50000 was invested at .0775/4= 0.019375. That earned (0.019375)(50000)= 968.75 interest. There is now 50968.75 in the account.

For the second quarter, 50968.75 was invested at 0.019375. That earned (0.19375)(50968.75)= 987.52 interest. There is now 51956.27 in the account.

Continue that for 10 more quarters to find the total amount in the account at the end f the three years. Subtract the original 50000 from the total amount to find the total interest earned.