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compounf interest

kaye

New member
Sep 7, 2021
2
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?
 

skeeter

Well-known member
MHB Math Helper
Mar 1, 2012
1,001
$A = A_0 \left(1 + \dfrac{r}{n}\right)^{nt}$

$A$ = account balance after $t$ years
$A_0$ = initial account balance
$r$ = annual interest rate as a decimal
$n$ = number of compounding periods per year
 

Prove It

Well-known member
MHB Math Helper
Jan 26, 2012
1,453
I tend to prefer not blindly substituting into a formula.

If the interest rate is 7.75% p.a. compounded quarterly, then the quarterly rate is 1.9375%.

So every quarter, you increase by 1.9375%, thus you end up with 101.9375%.

Thus the multiplier is 1.019375

If you're investing for 3 years, then that's 12 quarters.

Thus $\displaystyle A = 50\,000 \times \left(1.019\,375 \right)^{12} $.