1 Each year a single payment of 1766 is deposited into an ac

1. Each year a single payment of $1,766 is deposited into an account that earns 6 percent compounded continuously. After the fifth payment, the amount in the account is closest to:

2. A loan of $5,000 is made with a nominal interest rate of 6 percent per year compounded monthly. The amount of the equal monthly payment if someone wants to pay off the loan over 2½ years is closest to:

Solution

Ans 1)

Annual Payment of $1766 is deposited into account that earns 6% per year compounded continuously

to find amount in the account after 5th payment we will do it as following

Interest rate Compounding continuously will be done by exp(rt)-1 that is exponential of r which will give us continuously compounded rate

exp(0.06)-1=6.183%

hence Amount in account after 5 years will be calculated as

1766*exp(0.06(1))+1766*exp(0.06(2))+1766*exp(0.06(3))+1766*exp(0.06(4))+1766*exp(0.06(5))=1766*6.007=$10608.36

Hence amount will be close to $11,000