Compound Interest Problems

Exponents, Compound Interest (and the Second Most Famous Number in the Universe) A special case of exponential functions is compounding – or the increasing of money over time such that every time the invested money grows, the new amount is used to calculate interest. compounding interest formula:

r P= A1  n

nt

P = initial amount invested r = rate of interest n = # of times compounded (per year) t = # of years

1. If Jack invests $5,000 in an account at 6% interest, a) compounded monthly, what is his investment worth in 5 years? b) compounded daily, what is his investment worth in 5 years? c) How many seconds are there in a year? What is the answer if we compound the interest every single second for five years? d) What is the answer if we continuously compound the interest for five years? e) When will his investment be worth $10,000 if the interest is compounded continuously? Compounding continuously formula: rt P =Ae is the standard equation for continuous compounding 2. Grandpa Henry isn't sure which investment is better. Should he invest in a fund which pays 6.7% compounded monthly or a fund which pays 6.5% compounded continuously? 3. How long does it take for an account to double if it grows according to the model 0.035t ? P=25000 e 4. Aunt Hildegarde likes free gifts so when her bank gave away toasters, she invested $2,500in an account that is compounded daily at 3.2%. Unfortunately, Aunt Hildegarde was somewhat senile and she forgot about the account and when she died, you inherited it. If the money was untouched for 38 years, how much did you inherit?