Question

$5,000 is deposited today into a bank account. The account earns 6.2% per annum compounded half yearly for the first 7 years, then 6.1% per annum compounded quarterly thereafter. Assuming no further deposits or withdrawals are made,

(c) Calculate the account balance 7.5 years from today.

Answer 1

Calculation of account balance after 7.5 years

Given :- Principal Amount (P)---5000$

Rate of interest (R)---- 6.2% (for 7 years compounded half

Yearly)

(R) ------ 6.1% (for 0.5 year compounded quarterly)

Time (T) ------7.5 years ( 7 years 6 months)

Calculation for 7 years when interest compounded half yearly

Formula- Amount = P[1+(R/2)/100]2T

^{. Amount = 5000$[1+(6.2/2)/100]^2×7}

^{. Amount =5000$[1+3.1/100]^14}

^{. Amount = 5000$[103.1/100]^14}

^{. Amount = 5000$[1.031]^14}

^{. Amount = 5000$× 1.5332 ( Up to four decimal)}

^{. Amount = 7666$}

^{so, this amount is principal for next 0.5 year}

Calculation for 0.5 year when interest compounded quarterly

Formula Amount = P[1+(R/4)/100]4T

^{so, amoun = 7666$ is principal for next 0.5 year}

Amount = 7666$[1+(6.1/4)/100]^4×0.5

Amount = 7666$[1+ 1.525/100]^2

Amount = 7666$[1.0152]^2

Amount = 7666$ ×1.0306

Amount = 7900.57$

Account balance after 7.5 years =7900.57$