Question

Q5)

Selima deposits $5000 ( t = 0 years) in an account paying r(2) = 3.00%.At the end of 4 years (t = 4 years) she adds another $9000 to her account and the interest rate changes to r(2) = X%. After another 3 years ( t = 7 years) she adds another $7000 to her account and the interest changes to r(2) = 3.00%. At the end of 11 years, she has $27567.44 in her account.

a) How much money does she have in her account at t = 4 years just before she makes her deposit?

b) How much money does she have in her account after 7 years, just after she makes her deposit?

c) What is X%?

Answer 1

Deposit at t0 =$5000

FV at end of 4 years= 5000*(1+3%)^4=5000*1.03^4=5000*1.1255=$5627.54

Total amount at emd of 4 years=5627.54+9000=$14627.54

FV at the end of 7 years=14627.54*(1+x)^3

Total amount at the end of 7 years=14627.54*(1+x)^3+7000

FV at the end of 11 years=(14627.54*(1+x)^3+7000)*(1+3%)^4

Or, 27567.44=(14627.54*(1+x)^3+7000)*1.03^4

Or, 14627.54*(1+x)^3+7000=27567.44/1.1255

Or, 14627.54*(1+x)^3=24493.31-7000

Or, (1+x)^3=17493.31/14627.44

Or, 1+x=1.1959^(1/3)

Or,x=1.0615-1

Or,x=0.0615 or 6.15%

Amswer a: Amount at end of 4 year=$5627.54

Answer b: Amount at end of 7 years=5627.54*(1+6.15%)^3=5627.54*1.1959=$6730.98

Amount after deposit =6730.98+7000=$13730.98

Answer c:x=6.15%