Janesh has savings...

Question

Janesh has savings of $10,013.98. If he can invest this amount to earn 3.2%, how many days will it take for the investment to grow to $10,200? Also calculate the interest earned for this investment. (Do not round intermediate calculations. Round "Number of days" UP to the next whole day. Round "Interest earned" to 2 decimal places.)

Answer 1

First change the interest rate to days

1 + r = (1 + i)³⁶⁵

r = annual interest rate = 3.2% = 0.032
i = daily interest rate

Solve for i and get i = 0.000086301...
Store this value in your calculator.

Use the compound interest formula:

10200 = 10013.98 * (1+i)ⁿ

Where n = # of days

Solve for n.

10200/10013.98 = (1+i)ⁿ
log(10200/10013.98) = n * log(1+i)
n = log (10200/10013.98) / log (1+i) = 213.28...

Round UP and get 214 days.

Interest earned = Amount after 214 days - Original Amount = 10013.98(1+i)²¹⁴ - 10013.98 ≈ $186.65