Question

Selima deposits $8000 ( t = 0 years) in an account paying r(2) = 5.00%.At the end of 4 years (t = 4 years) she adds another $5000 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 $27721.81 in her account.

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

a.Amount befor the second deposit is

$$P(1+r)^n$$

$$8000(1+{5\over100})^4$$

$$=9724.05$$

b.

Amount after 3yrs at t=7

$$9724.05+50000=14724.05=p$$

$$14724.05(1+x)^7$$

c.

Value of x

$$14724.05(1+x)^7+7000(1+{3\over100})^{11}=27721.81$$

$$14724.05(1+x)^7+9689.63709=27721.81$$

$$14724.05(1+x)^7=18032.0.179$$

$$(1+x)^7=1.2474$$

$$1.0321=1+x$$

$$x=0.0321=3.21\%$$