Investment When Cleavon turned 5 years old, his grandmother decided it was time to start saving for his college education. She deposited $5000 in a special account earning 5% interest compounded continuously. By the time Cleavon begins college at the age of 18, his grandmother estimates that her grandson will need $40,000 for college tuition.
a. Approximate Cleavon's savings account balance on his 18th birthday using five terms of the exponential series.
b. Will the account have sufficient funds for Cleavon's college tuition by the time he is ready to start college? Explain.
c. Use a calculator to compute how long it will take the account to accumulate $40,000. How old would Cleavon be by this time?
d. To have at least $40,000 when Cleavon is 18 years old, how much should his grandmother have invested when he was 5 years old to the nearest dollar?