Question

1. An account was established 4 years ago with an initial deposit. Today the account is credited with annual interest of $291. The interest rate is 7.6% compounded annually. No other deposits or withdrawals have been made. How much is the end-of-day balance? 1. Construct the timelines. 2. Find the balance at the end of year 3. 3. Find the balance at the end of year 4.

Answer 1

1. Timeline for Compound Interest TO T1 → 72 T3 T4 Initial Deposit Interest Year 1 Value at Year 1 Interest Year 2 Value at Year 2 Interest Year 3 Value at Interest Year 3 $ 291 Value at Year 4 Compound interest @ 7.60 % per year

Interest for year 4 at compound interest @ 7.60%
= Value of investment at the end of Year 3 - Value of
investment at the end of year 3
Value of investment at the end of Year 3
A = P * ( 1 + R ) ^ N
where,
A = Value of investment
P = Principle amount
R = Rate of interest
N = period
	Year 3	Year 4
P	P	P
R	7.60%	7.60%
N	3	4
A = P * ( 1 + R ) ^ N	P * 1.2458	P * 1.3404
Interest for Year 4 = (P * 1.3404) - (P * 1.2458)
Interest for Year 4 = (P * (1.3404 - 1.2458)
Interest for Year 4 = (P * (0.0946)
As provided, Interest for Year 4 = $ 291
P * 0.0946 = $ 291
P = $ 291 / 0.0946
P = $ 3,076
2.
	Year 3
P	$3,076
R	7.60%
N	3
A = P * ( 1 + R ) ^ N	$3,832
Balance at the end of year 3 = $ 3,832
3.
	Year 4
P	$3,076
R	7.60%
N	4
A = P * ( 1 + R ) ^ N	$4,123
Balance at the end of year 4 = $ 4,123