Question

Tim has a savings account with the bank. The bank pays him 1% per year. He has $5,000 and wonders when it will reach $5,300. When will his savings reach $5,300? If necessary, round the answer to the nearest whole number.

Considering interest is calculated yearly, it will take Tim approximately ___ year(s).

Answer 1

Assume interest is compounded at the end of each year, with a principal P over n years at interest i=0.01.
Future value =5300

Then
Future value
= P(1+i)^n
=>
5300=5000((1.01)^n)

Solve for n
1.01^n=5300/5000=1.06
n=1.06^(1/6)=5.856 years.


If interest rate is 1% simple interest, then
n=(1.06-1)/.01=6 years.

Answer 2

If interest is calculated yearly, it will take Time approximately 6 years

Explanation:

For interest compounded continuously we use this formula

A =
`pe^(rt)`

Where A = Amount in future ($5,300)

P = Principal amount ($5,000)

r = interest rate (1% or 0.01)

t = time

Now we put the values

5300 = 5000e
`^((0.01)t)`

1.06 =
`e^((0.01)t)`

㏑1.06 = 0.01t

t = ㏑(2) ÷ 0.01

t = 5.82 years rounded to 6 years

If interest is calculated yearly (simple interest)

n = ( 1.06-1 ) / 0.01 = 6 years.

If interest is calculated yearly, it will take Time approximately 6 years.