Question #117578

without using finance calculator,

(a) Haziq invests RM15,000 in a fund at 7% compounded quarterly. After t years, the value of the investment is RM300,000. Determine the value of t.

(b) Sarah invested RM5000 into an account that pays 5% compounded semiannually. She intended to keep the account untouched for 5 years. However, after 3 years, she had to withdraw RM3000. Find the amount left in the account after five years from the time she made her investment.

(a) Haziq invests RM15,000 in a fund at 7% compounded quarterly. After t years, the value of the investment is RM300,000. Determine the value of t.

(b) Sarah invested RM5000 into an account that pays 5% compounded semiannually. She intended to keep the account untouched for 5 years. However, after 3 years, she had to withdraw RM3000. Find the amount left in the account after five years from the time she made her investment.

Expert's answer

a) After t years initial investment of RM15,000 would have value:

"15 000*(1+0.07\/4)^{4t}=300000"

which means that:

"1.0175^{4t}=20"

"t=\\frac{\\log_{1.0175}20}{4}"

"t\\approx43.169" years

b) After three years Sarah had in her account the following sum:

"5000*(1+0.05\/2)^6"

After withdrawal of 3 000 she had:

"5000*(1+0.05\/2)^6-3000"

After two more years (i.e. five years she made her investment) she had:

"[5000*(1+0.05\/2)^6-3000]*[1+0.05\/2]^4\\approx3088.984" RM

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