Question

1) a) b) c) d) Claire's grandfather had opened a savings account in her name when she turned 13 years of age, and deposited $5,000 in it then. Claire is now 28 years of age If the account paid interest at the rate of 4.5% per year, how much money will Claire be able to withdraw from the account todav? If Claire would like to withdraw S10,000 today, what interest rate should she have earned on the account? If the account paid interest at the rate of 5% per year, how many years will it take for the money to grow to become $12,000 from the time it was deposited? If the account paid interest at the rate of 4.5% per year for the first 10 years, and then the interest rate increased to 5.5% per year, how much will be in the account today? 2) a) b) Jay's brother has offered to give him either $5,000 today or $7,000 in 4 years If the opportunity cost of both options is 7% per year, which option should Jay choose? At what opportunity cost will Jay be indifferent between the two options?

Answer 1

(1)

(a) Deposit was made when Claire Turned 13 and today she is 28. This implies an investment tenure of (28 - 13) = 15 years

Deposit Amount = $ 5000 and Interest Rate = 4.5 %

Therefore, Final Account Value = 5000 x (1.045)^(15) = $ 9676.41

(b) Final Value of Account = $ 10000 and Initial Deposit = $ 5000

Let the interest rate be R

Therefore, 5000 x (1+R)^(15) = 10000

(1+R)^(15) = 2

R = (2)^(1/15) - 1

R = 0.04729 or 4.73 %

(c) Initial Deposit = $ 5000, Final Required Deposit Value = $ 12000 and Interest Rate = 12 %

Let the required number of years be N

Therefore, 5000 x (1.05)^(N) = 12000

(1.05)^(N) = 12000 / 5000

(1.05)^(N) = 2.4

N = $\log_{1.05} 2.4$ = 17.94 years ~ 18 years

(d) Initial Deposit Value = $ 5000, Initial Interest Rate = 4.5 % and Final Interest Rate = 5.5 %

Therefore, Final Account Value = 5000 x (1.045)^(10) x (1.055)^(2) = $ 8642.469 ~ $ 8642.47

NOTE: Please raise separate queries for solutions to the remaining unrelated questions as one query is restricted to the solution of only one complete question (with a maximum of four sub-parts)